8.3a-vectors 33 22 11 terms operations practice problems
TRANSCRIPT
8.3a-Vectors
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2
1Terms
Operations
Practice Problems
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What are Vectors Used For?
Vectors represent Paths of travel
i.e. distances Velocity
Direction and speed of an object Forces
WeightPressure
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Terms
Vector Directed line segment
Similar to a line or ray Has direction
Can be designated by: Ordered pairs Radians Degrees Graphically
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Terms (Cont.)
Vector (Cont.) Has Magnitude
How long the vector is Basically, the hypotenuse of a triangle if it is
not purely vertical or horizontal
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Notation
Ordered Pair Form Same as ordered pairs except <> is used
instead of ()
1,2
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Notation (Cont.)
Vector Name When possible use named points
Starting point is listed 1st
Ending point is listed 2nd
Arrow is placed over the lettersEx.
If no named points are available, “u” and “v” are typical
AB
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Notation (Cont.)
Vector Example
P
Q
PQ
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Notation (Cont.)
Magnitude Amount of force, weight, velocity, etc. Represented by:
Vector NameEnclosed by double vertical lines
PQ
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Addition/Subtraction of Vectors Combines the elements of 2 or more
vectors Result is called a Resultant Vector
7,24,3
74,23
3,5
1,51,5
11),5(5
0,10
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Graphic Representation of Vector Addition/Subtraction
Align vectors end-to-end without changing the angle
Draw a new vector from the beginning of the first vector to the end of the last vector
Name the resultant vector according to beginning and ending points
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Graphic Example of Addition of Vectors
AB
BC
ACBCAB
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Scalar Multiples
Changes the magnitude But not the angle Steps
Multiply each component of the vector by the scalar (number)
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Scalar Multiples Examples
4,32
)4(2),3(2
8,6
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Finding the Magnitude
Steps Square each element of the vector Add Take the square root Basically the Pythagorean Theorem
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Finding the Magnitude (Cont.)Find the Magnitude of
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i & j Coordinate System
In plain English…i is the x-axis, and j is the y-axis
ji 252,5
ji 434,3
jji 6606,0
iji 110110,11
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i and j Coordinate Example
Treat i and j as if they were variables
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Practice Problems
Page 601Problems 1-10, 29-36