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# Scalar Multiplication

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1.
If $vec{u}=<< 1,-4 >>$, what is the value of $-1vec{u}$ ?
1. $<< 1,-4 >>$
2. $<< 0,-5 >>$
3. $<< 2,-2 >>$
4. $<< -1,4 >>$
2.
Which of the following is equivalent to $4<<3,-1>> ?$
1. $<<12,-4>>$
2. $<<12,-1>>$
3. $<<7,3>>$
4. $<<3,-4>>$
3.
For $vec{v} = <<-3, 8>>$, which of the following is equal to $-3vec{v} ?$
1. $<<-6,8>>$
2. $<<-9,8>>$
3. $<<9,-24>>$
4. $<<-27, 24>>$
4.
If $a = -1/2$ and $vec{w} = <<6,-1>>$, choose the correct value of $a \ vec{w}$.
1. $<<-3,1/2>>$
2. $<<3,1>>$
3. $<<-3,-1>>$
4. $<<-3/2, -1/2>>$
5.
If you multiply $vec{u}=<< 14,10 >>$ by a scalar and the result is $vec{u}=<< 7,5 >>$, what is the scalar?
1. $2$
2. $-5$
3. $-7$
4. $1/2$
6.
If $vec{n} = <<4,8>>$, and $a \ vec{n} = <<1,2>>$, what is the value of $a ?$
1. $4$
2. $1/4$
3. $1/2$
4. $2$
7.
If $-a \ vec{v} = <<-9,12>>$ and $a \ vec{v} = <<9,-12>>$, and $a$ can be any real number (positive or negative), which of the following are possible values of $vec{v} ?$ Choose all that apply.
1. $<<9,12>>$
2. $<<3,-4>>$
3. $<<-3,-4>>$
4. $<<-9,12>>$
8.
If $vec{u}$ has its initial point at the origin, and its terminal point at $(3,4)$, where will its terminal point be if $vec{u}$ is multiplied by -2 ? Assume that its initial point remains at the origin.
1. $(6,8)$
2. $(-6,8)$
3. $(6,-8)$
4. $(-6,-8)$
9.
Draw the vector $vec{v} = <<-2,-4>>$ with its initial point at the origin. Then, draw $-1/2 vec{v}$, also with its initial point at the origin.
• See graph. First vector should terminate at $(-2,-4)$, second vector should terminate at $(1,2)$.
10.
Draw the vector $vec{u} = <<3,-2>>$ with its initial point at the origin. Then, draw $3vec{u}$ also with its initial point at the origin.
• See graph. Vectors will be overlapping. $vec{u}$ should terminate at $(3,-2)$, and $3vec{u}$ should terminate at $(9,-6)$.
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