##### Notes

This printable supports Common Core Mathematics Standard HSN-VM.A.4, HSN-VM.A.4a

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1.
Let the triangle below represent the vectors $vec{AB}, vec{BC},$ and $vec{AC}$. Then, $vec{AB} + vec{BC} = vec{AC}$.
1. True
2. False
2.
Let the triangle below represent the vectors $vec{AB}, vec{AC}$, and $vec{BC}$. Then $vec{AB} + vec{AC} = vec{BC}$
1. True
2. False
3.
When adding vectors graphically using the head-to-tail method, always ensure that the their initial points are coincident.
1. True
2. False
4.
For $vec{a} = <<4,-2>>$ and $vec{b} = <<3,7>>$ find $vec{a} + vec{b}$ by graphing. Ensure that the vector $vec{a} + vec{b}$ starts at the origin.

5.
For $vec[m} = <<-3,8>>$ and $vec{n} = <<3,-2>>$, find $vec{m} + vec{n}$ graphically. Ensure that the vector $vec{m} + vec{n}$ starts at the origin.

6.
Find the sum of the vectors $vec{A} = <<-3,-4>>$ and $vec{B} = <<7,8>>$ graphically using any method.

7.
For $vec{v} = <<3,-5>>$ and $vec{w} = <<-2,-1>>$, find $vec{v} + vec{w}$.
1. $<<5,6>>$
2. $<<1,-6>>$
3. $<<5, -4>>$
4. $<<1,-4>>$
8.
Find the sum. $<<15,-4>> + <<3, 4>>$
1. $<<18, 8>>$
2. $<<12,8>>$
3. $<<18,0>>$
4. $<<11,7>>$
9.
Evaluate. $<<-4,6>> + <<-3,4>>$
1. $<<2,1>>$
2. $<<-1,10>>$
3. $<<-1,2>>$
4. $<<-7,10>>$
10.
For $vec{w}$ and $vec{v}$, is it true that $||vec{w} + vec{v}||$ is NEVER equal to $||vec{w}||+||vec{v}|| ?$ Why or why not?
1. Yes this is true. Since the magnitude of a vector involves taking a square root, and you cannot distribute a square root over multiple terms, this can never be true.
2. Yes this is true. For example, let $vec{u} = <<5,2>>$ and $vec{v}=<<2,3>>$.
3. No, this is not true; there are times when they are equal. Looking at the vectors geometrically, and applying the law of cosines (where the sides are the magnitudes of the vectors), it can be proved that the magnitude of the sums of the vectors are in certain cases equal to the sum of the magnitudes (using some trigonometric identities).
4. No, this is not true; there are times when they are equal. For example, let $vec{u} = <<0,2>>$ and $vec{v}=<<0,3>>$.
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