warm up 1. find the magnitude of this vector 2. a vector has initial point (0,2) and terminal point...
TRANSCRIPT
Warm up
1. Find the magnitude of this vector<-3,15> 2. A vector has Initial point (0,2) and terminal point (9,15). Write this vector in component form.3. Find the angle this vector makes with it’s horizontal. <3,7> 4. Find the dot product of <-7,12> and <0,-3>
ESSENTIAL QUESTION
What is a Unit Vector, and how do I graph a vector in component form?
Math IV Lesson 54 Vectors • Standard: MCC9 12.N.VM.1(+)Recognize vector quantities as ‐
having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v , | v|,||v||,v).
Example: Graph vector <3,9>
Multiples of Vectors
Given a real number c, we can multiply a vector by c by multiplying its magnitude by c:
v2v -2v
Notice that multiplying a vector by anegative real number reverses the direction.
Find and graph the following3u-3u1/4u
Addition
To add vectors, simply add their components.
For example, if v = <3,4> and w = <-2,5>, then v + w = <1,9>.
Other combinations are possible. For example: 4v – 2w = <16,6>.
Magnitude
The magnitude of the vector is the length of the segment, it is written ||v||.
v
(2,2)
(5,6)
Unit Vectors
A unit vector is a vector with magnitude 1.Example <3/5, 4/5> is a unit vector.
Given a vector v, we can form a unit vector by multiplying the vector by 1/||v||.
For example, find the unit vector in the direction <3,4>:
Unit Vectors Notation
A vector such as <3,4> can be written as
3<1,0> + 4<0,1>.
For this reason, these vectors are given special names: i = <1,0> and j = <0,1>.
A vector in component form v = <a,b> can be written ai + bj.
WRITE THIS VECTOR USING UNIT VECTOR NOTATION
<7,-12>
Heroic QuestHeroic Quest1. Graph this vector <3,-2> 2. Make a unit vector in the same direction as <3,-
2>. 3. Write <3,-2> in unit vector form4. Given u = <3,2> and u = <7,3> Find the dot
product of the two vectors