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What are the characteristics of the letters that are commonly used to represent vectors?
lowercase, bold letter, usually u,v,w
How is a vector more specific than a line segment?
What are i and j, and what do they represent?
They are unit vectors. They are used to represent the horizontal and vertical components of a vector. They each have a magnitude of 1.
What is component form?
When a unit vector is expressed as ⟨a,b⟩, which letter is the coefficient of the i and which the j?
The first number always represents the coefficient of the i, and the second represents the j.
Given a vector with initial point (5,2) and terminal point (−1,−3), find an equivalent vector whose initial point is (0,0). Write the vector in component form ⟨a,b⟩.
Given a vector with initial point (−4,2) and terminal point (3,−3), find an equivalent vector whose initial point is (0,0). Write the vector in component form ⟨a,b⟩.
〈7,−5〉
Given a vector with initial point (7,−1) and terminal point (−1,−7), find an equivalent vector whose initial point is (0,0). Write the vector in component form ⟨a,b⟩.
For the following exercises, determine whether the two vectors u and v are equal, where u has an initial point P1 and a terminal point P2 and v has an initial point P3 and a terminal point P4 .
P1=(2,−3),P2=(5,1),P3=(6,−1), and P4=(9,3)
P1=(3,7),P2=(2,1),P3=(1,2), and P4=(−1,−4)
Given initial point P1=(−3,1) and terminal point P2=(5,2), write the vector v in terms of i and j.
Given initial point P1=(6,0) and terminal point P2=(−1,−3), write the vector v in terms of i and j.
7i−3j
For the following exercises, use the vectors u = i + 5 j , v = −2 i − 3 j , and w = 4 i − j .
Find u + ( v − w )
For the following exercises, use the given vectors to compute u + v , u − v , and 2 u − 3 v .
u=⟨2,−3⟩,v=⟨1,5⟩
Let v = −4 i + 3 j . Find a vector that is half the length and points in the same direction as v.
Let v = 5 i + 2 j . Find a vector that is twice the length and points in the opposite direction as v.
−10i–
For the following exercises, find a unit vector in the same direction as the given vector.
a = 3 i + 4 j
c = 10 i – j
u = 100 i + 200 j
For the following exercises, find the magnitude and direction of the vector,
Given u = 3 i − 4 j and v = −2 i + 3 j , calculate
Given and calculate
For the following exercises, given draw 3 v and
For the following exercises, use the vectors shown to sketch u + v , u − v , and 2 u .
For the following exercises, use the vectors shown to sketch 2 u + v .
For the following exercises, use the vectors shown to sketch u − 3 v .
For the following exercises, write the vector shown in component form.
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