##### Notes

This printable supports Common Core Mathematics Standard HSN-VM.B.4, HSN-VM.B.4c

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## Vector Subtraction

1.
Which of the following are equivalent to $vec{a} - vec{b} ?$ Choose all that apply.
1. $vec{a} + (-vec{b})$
2. $vec{b} - vec{a}$
3. $-vec{a} + vec{b}$
4. $-vec{b} + vec{a}$
2.
Which of the following is the additive inverse of $vec{v} = <<-4,6>> ?$
1. $<<4,6>>$
2. $<<1/4, -1/6>>$
3. $<<-1/4, 1/6>>$
4. $<<4,-6>>$
3.
For $vec{a} = <<4,8>>, \ \ vec{b} = <<1,7>>$, find the difference, $vec{a} - vec{b}$.
1. $<<-3, 7>>$
2. $<<-4,-6>>$
3. $<<3,1>>$
4. $<<5,15>>$
4.
If vector $vec{t} = < 13,28 >$ and vector $vec{r} = < -13,-28 >$, what is the result of $vec{t} - vec{r}$ ?
1. $< -26,-56 >$
2. $< 0,0 >$
3. $< 26,56 >$
4. $< 41,-41 >$
5.
If vector $vec{v} = < -3,14 >$ and vector $vec{w} = < -8,8 >$, what is the result of $vec{w} - vec{v}$ ?
1. $< 11,-22>$
2. $< 5,6 >$
3. $< -11,0 >$
4. $< -5,-6 >$
6.
Let triangle ABC represent vectors $vec{AB}, vec{CB}, vec{AC}$. Then $vec{AB} - vec{CB} = vec{AC}$.
1. True
2. False
7.
For $vec{n} = <<-3,6>>$ and $vec{m} = <<4,-2>>$, find $vec{n} - vec{m}$ graphically.

8.
For $vec{a} = <<5,1>>$ and $vec{b} = <<-3,-4>>$, find $vec{b} - vec{a}$ graphically.

9.
For vectors $vec{v}$ and $vec{w}$, if one were to find $vec{w} - vec{v}$ graphically, which of the following could be true? Choose all that apply.
1. The heads of the vectors would be touching.
2. The tails of the vectors would be touching.
3. The head of vector $vec{w}$ would touch the tail of vector $vec{v}$.
4. The head of vector $vec{v}$ would touch the tail of vector $vec{w}$.
10.
Given two vectors, $vec{v}$ and $vec{w}$, which are opposite in direction and where $||vec{v}|| = 2||vec{w}||$. What does $vec{v}-vec{w}$ equal? Choose all that apply.
1. $1/2 vec{v}$
2. $3/2 vec{v}$
3. $-3vec{w}$
4. $vec{0}$
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