Download - Physics M1 Vectors
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXBefore you begin, see diagram below. Look for the Security Warning below the ribbon and click the Options button. In the Security Alert box, select “Enable this Content”. Click OK.
BEGINBEGIN
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XX
Physics Module 1 Unit 1 Lessons 16-17
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XX
The diagram shows Tom about to drive out of a parking lot in his community.
1. What is Tom’s direction from the house?
2. What Tom’s distance from the house?
3. What is Tom’s distance from the school?
INTRODUCTION
1. South East
2. 250 m
3. 180 m
3
100 m
150 m 80 m
Tom’s car
house school
CHECKCHECKCHECKCHECK
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XX
Tom in his community cont’d
4. What directions would Tom take in order to get the house by road?
5. What direction could Tom take to go in a straight line to the house?
6. Is the distance to go straight to the house shorter or longer than by road?
INTRODUCTION
4. North then West
5. Northwest
6. Shorter
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100 m
150 m 80 m
Tom’s car
house school
CHECKCHECKCHECKCHECK
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXINTRODUCTION
http://www.mrfizix.com/home/vectors.htm
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OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXOBJECTIVES
When you complete this slide presentation, you will be able to:•Represent vectors graphically;•State three ways in which the directions of vectors are written•Draw vectors based on their definitions•Explain what is meant by the negative of a vector.•Draw the negatives of given vectors•Determine the magnitude and direction of the resultant parallel and anti-parallel vectors•Use the Pythagoras' theorem to calculate resultant vectors which perpendicular•Determine the resultant of vectors that are neither parallel nor anti-parallel using scale drawings.•Use the parallelogram method to determine the resultant of concurrent vectors
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OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXHow do you represent a vector quantity
graphically?
A vector quantity that has both magnitude and a specified direction.
A vector quantity is represented graphically by a straight line with an arrowhead.
The arrowhead points in the direction of the vector and the length of the line is proportional to the magnitude of the vector
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Head of vector
Tail of vector
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXWhat are the ways of writing the
direction of a vector quantity?
8
W
S
N
E
S
N
1300
Boat travels with velocity of 15 m/s North East
Helicopter travels 200 km on a bearing of 130o
COMPASS POINT BEARINGS
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXWhat are the ways of writing the
direction of a vector quantity?
9
300
Rocket flies with acceleration of 12 m/s2 vertically upwards
Aircraft flies with velocity of 35 m/s at 30o above the horizontal
RELATIVE TO THE VERTICAL AND HORIZONTAL
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XX
Click on the number to reveal the step.
3
2
1
How can these vectors be represented? The Steps
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Choose a suitable scale that would give a reasonable length line. For example: If a scale of 1 cm: 100 km was chosen for the helicopter vector, the line representing vector would have length 200/ 100 = 2 cm which is too short. If it was 1cm : 5 km the line representing the vector would have length 200/5 = 40 cm which is too long.
Choose a suitable scale that would give a reasonable length line. For example: If a scale of 1 cm: 100 km was chosen for the helicopter vector, the line representing vector would have length 200/ 100 = 2 cm which is too short. If it was 1cm : 5 km the line representing the vector would have length 200/5 = 40 cm which is too long.
Draw the line of length 10 cm at a bearing of 130o using a protractor to measure the angle.Draw the line of length 10 cm at a bearing of 130o using a protractor to measure the angle.
Put an arrowhead on the line to show the direction and label the line with the magnitude of vector and NOT the length of the line.
Put an arrowhead on the line to show the direction and label the line with the magnitude of vector and NOT the length of the line.
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXHow are the vectors represented?
Here is the way the vectors mentioned can be represented:
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S
N
1300
200 km
300
35 m/s
Length of vector: 10 cmDirection: 130o
Scale 1cm: 20 km
Length of vector: 7 cmDirection: 30o above the horizontal
Scale 1cm: 5 m/s
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXHow do you represent a vector quantity
graphically?
Draw scale diagrams of the following vectors:1. A ship travels 20 km at 40o West of North
2. A canoe travels with velocity 2.0 m/s on a bearing of 130o
3. A boy pushing a trolley, with a force of 70 N at an angle of 30o below the horizontal.
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Click here to check your answer
Click here to check your answer
Click here to check your answer
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXNegative of a Vector
The negative of a vector is another vector of same magnitude as the vector but of opposite direction.
The vector – p is the negative of the vector p.
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p
– p
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXNegative of a Vector
State the magnitude and direction of the negative of the vector 2.0m/s on a bearing of 130o .
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S
N
310o
2.0 m/s
2.0 m/s
Negative of the vector is 2.0 m/s on a bearing of 310o
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXNegative of a Vector
State the magnitude and direction of the negative of the vector 20 km at 40o West of North
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W
S
N
E
40020 km
20 km
500
Negative of the vector is 20 km at 50o South of East
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXCan vectors be added?
When two vectors are added, the sum vector is called the resultant. There are two methods of adding vectors
1. Head to tail method. Used with free vectors.
2. Parallelogram method. Used with concurrent vectors
Only vectors representing quantities with the same units can be added.The magnitude and direction of a resultant vector can either be found by scale drawing or calculation.
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OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XX Adding Vectors
Parallel and Anti-parallel Vectors
1. Adding two parallel vectors
2. Adding two anti-parallel vectors
When adding parallel vectors, add the magnitudes of the vectors. The direction of the resultant is the same as the vectors. When adding anti-parallel vectors, subtract the magnitudes. The direction of the resultant is in the direction of the vector of greater magnitude.20
2 m/s 5 m/s
7 m/s
2 m/s 5 m/s
3 m/s
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXAdding Vectors: Vectors that are neither
parallel nor anti-parallel
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100 m
150 m80 m
Tom’s car
house school
Recall in the introductory activity that Tom could get to his house two ways. One way is to drive 100 m North together with 150 m West. The other way (which is not possible) is to drive directly from the parking lot to his gate
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXAdding Vectors: Vectors that are neither
parallel nor anti-parallel
The single resultant vector that would take Tom to his house has the same effect as the two vectors put head to tail.
When adding vectors that are neither parallel nor anti-parallel, place the vectors head to tail and the vector that is drawn from the tail of the first vector to the head of the second vector is the resultant of the two vectors.
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OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XX
Problem: What is the distance and direction of Tom’s house from the parking lot? To answer the question, the magnitude of the vector R and the angle θ must be found.
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Adding Vectors: Vectors that are neither parallel nor anti-parallel
100 m
150 m
R
Mathematical solutionUsing Pythagoras’ equationR2 = 1002 + 1502
= 10000 + 22500 = 32500R = √32500 = 180 m
Tan θ = 150/100 = 1.5 θ = tan-1 1.5 = 56.3o
θ
AnswerTom’s house is 180 m from the parking lot in a direction of 56.3o West of North.
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXAdding Vectors: Vectors that are neither
parallel nor anti-parallel Fill in the blank spaces in the instructions for a scale drawing to find the distance and direction of the house1.Choose a suitable scale of 1 cm : 10 m2.Draw a line of length ____ cm with arrowhead pointing in the ________ direction to represent the 100 m vector, and a line of length ______ cm with arrowhead pointing in the ________ direction to represent the 150 m vector.3.The tail of the 150 m vector must be joined to the head of the 100 m vector.4.Draw a line from the tail of the 100 m vector to the head of the 150 m vector. 5.Measure the length of the line and multiply the result by _____ for the length of the vector in m.6.Measure the angle _____ with a protractor.7.Complete a drawing for yourself.
24Click for answers
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XX
25
Adding Vectors: Vectors that are neither parallel nor anti-parallel
Fill in the blank spaces in the instructions for a scale drawing to find the distance and direction of the house1.Choose a suitable scale of 1 cm : 10 m2.Draw a line of length 10 cm with arrowhead pointing in the North direction to represent the 100 m vector, and a line of length 15 cm with arrowhead pointing in the West direction to represent the 150 m vector.3.The tail of the 150 m vector must be joined to the head of the 100 m vector.4.Draw a line from the tail of the 100 m vector to the head of the 150 m vector. 5.Measure the length of the line and multiply the result by 10 for the length of the vector in m.6.Measure the angle θ with a protractor.7.Complete a drawing for yourself.
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXAdding Vectors: Concurrent Vectors
Concurrent vectors are vectors that originate at the same point or their lines of action intersect.
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Forces on the boat are concurrent because they are applied at the same point
Forces on the boat are concurrent because their lines of action intersect
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXAdding Vectors: Concurrent Vectors
Completing the Parallelogram Method
1. Open the compass to the length of one vector.
2. Place the compass point at the head of the other vector and draw an arc.
3. Repeat with the other vector and draw an intersecting arc.
4. Draw the resultant vector from the origin of the two vectors to the point of intersection of the arcs.
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Click to see method
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XX
Adding VectorsActivity 2.2
In the illustration the helicopter heads in the direction shown with velocity of 50 m/s and a cross wind blows with a velocity of 20 m/s. Use a scale drawing to determine the magnitude and direction of the resulting velocity of the helicopter.
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300
N
wind
W
Click for answer
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXAdding Vectors
Feedback to Activity 2.21. Choose a suitable scale2. Draw vector of length 10 cm
pointing 30o to North (helicopter vector)
3. Draw vector of length 4 cm at the head of the helicopter vector pointing west (wind vector).
4. Draw a vector from tail of the helicopter vector to the head of the wind vector. This is the resultant vector
5. Measure the length of the resultant vector and multiply the length by 5 to get the magnitude of the resultant in m/s
6. Measure the angle from North of the resultant 29
50 m/s
20 m/s
Scale 1 cm : 5 m/s
300
The resultant velocity of the The resultant velocity of the helicopter is 62.5 m/s at 46helicopter is 62.5 m/s at 46oo East of NorthEast of North
12.5 cm x 5 N/cm = 62.5 N46o
62.5 m/s
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XX
Adding VectorsActivity 2.3
In the illustration the forces of two ropes tied to the boat act on the boat. Use scale drawing to determine the magnitude of the resultant force on the boat. State the direction in which the boat will move relative to the 160 N force.
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160 N 240 N
Click to check your answer.
110o
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XX
Adding Vectors
1. Choose a suitable scale.2. Draw a force vector of length
8 cm to represent the 160 N force
3. Use the protractor to measure an angle of 110o and draw a force vector of length 10 cm to represent the 200 N force.
4. Use compasses to draw arcs.5. Draw the resultant vector6. Measure the length of the
vector and calculate its magnitude in N by multiplying the length by 20
7. Measure the angle between the resultant vector and the 160 N force
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110o
160 N 200 N
Scale 1 cm : 20 N
The magnitude of the resultant force on the boat is 210 N at 63.5o to the 160 N force.
210 N
63.5o
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXQUIZ
1. Are you ready to test yourself? 2. There are seven multiple choice items that
you are required to do. 3. For each item, click on the letter of the
correct response and then click the button ‘NEXT QUESTION’ to continue.
4. Click the BEGIN QUIZ button to start the quiz.
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BEGIN QUIZ!BEGIN QUIZ!
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXQUIZ: Question 1
Which one of the following is the best example of a vector quantity?
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A. A current of 5 A flowing from positive to negative
A. A current of 5 A flowing from positive to negative
B. A distance of 200 km from Kingston to Montego Bay
B. A distance of 200 km from Kingston to Montego Bay
C. A speed of 12 m/s around a bendC. A speed of 12 m/s around a bend
D. A force of 50 N to the rightD. A force of 50 N to the right
FEEDBACKFEEDBACKFEEDBACKFEEDBACK
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXQuiz: Feedback to Question 1
Which one of the following is the best example of a vector quantity?
34NEXT QUESTIONNEXT QUESTIONNEXT QUESTIONNEXT QUESTION
A is incorrect: Positive to negative does not state a specific directionB is incorrect: Kingston to Montego Bay does not state a specific directionC is incorrect: Direction changes continuously when going around a bend. It is not specific.D is correct: To the right is a specific direction that can be given relative to a known direction.
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XX
Two forces are applied to a body, as shown. What is the magnitude of the resultant force acting on the body?
QUIZ: Question 2
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A. 19N A. 19N
D. 10.9N D. 10.9N
C. 7N C. 7N
B. 13N B. 13N
FEEDBACKFEEDBACKFEEDBACKFEEDBACK
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXQuiz: Feedback to Question 2
Two forces are applied to a body, as shown. What is the magnitude of the resultant force acting on the body?
36NEXT QUESTIONNEXT QUESTIONNEXT QUESTIONNEXT QUESTION
The forces are perpendicular vectors R2 = F1
2 + F22 R2 = 52 +122
R = 144 25 169 13N
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXQUIZ: Question 3
Which correctly states the magnitude and direction of the resultant force on the train carriage in the diagram?
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A. 160 N to the leftA. 160 N to the left
D. 1160 N to the rightD. 1160 N to the right
B.920 N to the right B.920 N to the right
C. 840 N to the rightC. 840 N to the right
FEEDBACKFEEDBACKFEEDBACKFEEDBACK
1000 N
80 N80 N
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXQuiz: Feedback to Question 3
Which correctly states the magnitude and direction of the resultant force on the train carriage in the diagram?
38NEXT QUESTIONNEXT QUESTIONNEXT QUESTIONNEXT QUESTION
A is incorrect: It states the resultant force to the left onlyB is incorrect: It states the resultant force between the 1000 N and one of the 80 N forcesC is correct: It states the resultant force between the 1000 N and the two 80 N forces. D is incorrect: The forces in opposite directions are added and not subtracted.
1000 N
80 N80 N
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXQuiz: Question 4
A vector is defined as 2.0 m/s heading North West. Which best states the negative of this vector?
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A. 2.0 m/s heading South WestA. 2.0 m/s heading South West
D. 2.0 m/s heading North D. 2.0 m/s heading North
C. 2.0 m/s heading North EastC. 2.0 m/s heading North East
B. 2.0 m/s heading South East B. 2.0 m/s heading South East
FEEDBACKFEEDBACKFEEDBACKFEEDBACK
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXQuiz: Feedback to Question 4
A vector is defined as 2.0 m/s heading North West. Which best states the negative of this vector?
40NEXT QUESTIONNEXT QUESTIONNEXT QUESTIONNEXT QUESTION
The diagram shows the negative of the vector. A. C and D are incorrect. The negative of the vector is in the South East direction.
W
S
N
E
2.0 m/s
2.0 m/s
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXQUIZ: Question 5
Which is the correct way to subtract vector A from vector B that are neither parallel nor anti-parallel?
41
B. Add vector A to vector B and multiply the magnitude of the resultant by – 1.
B. Add vector A to vector B and multiply the magnitude of the resultant by – 1.
D. Subtract the magnitude of vector A from the magnitude of vector B.
D. Subtract the magnitude of vector A from the magnitude of vector B.
C. Add vector A to vector B and find the negative of the resultant vector
C. Add vector A to vector B and find the negative of the resultant vector
A. Add the negative of vector A to vector BA. Add the negative of vector A to vector B
FEEDBACKFEEDBACKFEEDBACKFEEDBACK
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXQuiz: Feedback to Question 5
Which is the correct way to subtract vector A from vector B that are neither parallel nor anti-parallel?
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A is correct: Subtraction of vectors is the same as adding the negative of one vector to the otherB is incorrect: This would only be making the magnitude of the sum of the vectors negative.C is incorrect: This would give the negative of the sum of the vectors and not the difference between them.D is incorrect: This is only applicable when vectors are parallel
END OF QUIZ END OF QUIZ END OF QUIZ END OF QUIZ
OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXEnd of Quiz
You have reached the end of the quiz. If you wish to review this lesson, go to the first
slide.If you have finished viewing the lesson, click the
Close (X) button.
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OBJECTIVESOBJECTIVES
Representing a vector quantity
graphically
Representing a vector quantity
graphically
Adding VectorsAdding Vectors
QUIZQUIZ
INTRODUCTIONINTRODUCTION
XXReference
www.phy.syr.edu/courses/.../PHY_101_Chapter_2_Lectures.ppt
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