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Scalar Multiplication

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Scalar Multiplication Answer Key

1. 
If [math]vec{u}=<< 1,-4 >>[/math], what is the value of [math]-1vec{u}[/math] ?
  1. [math]<< 1,-4 >>[/math]
  2. [math]<< 0,-5 >>[/math]
  3. [math]<< 2,-2 >>[/math]
  4. [math]<< -1,4 >>[/math]
2. 
Which of the following is equivalent to [math]4<<3,-1>> ?[/math]
  1. [math]<<12,-4>>[/math]
  2. [math]<<12,-1>>[/math]
  3. [math]<<7,3>>[/math]
  4. [math]<<3,-4>>[/math]
3. 
For [math]vec{v} = <<-3, 8>>[/math], which of the following is equal to [math]-3vec{v} ?[/math]
  1. [math]<<-6,8>>[/math]
  2. [math]<<-9,8>>[/math]
  3. [math]<<9,-24>>[/math]
  4. [math]<<-27, 24>>[/math]
4. 
If [math]a = -1/2[/math] and [math]vec{w} = <<6,-1>>[/math], choose the correct value of [math]a \ vec{w}[/math].
  1. [math]<<-3,1/2>>[/math]
  2. [math]<<3,1>>[/math]
  3. [math]<<-3,-1>>[/math]
  4. [math]<<-3/2, -1/2>>[/math]
5. 
If you multiply [math]vec{u}=<< 14,10 >>[/math] by a scalar and the result is [math]vec{u}=<< 7,5 >>[/math], what is the scalar?
  1. [math]2[/math]
  2. [math]-5[/math]
  3. [math]-7[/math]
  4. [math]1/2[/math]
6. 
If [math]vec{n} = <<4,8>>[/math], and [math]a \ vec{n} = <<1,2>>[/math], what is the value of [math]a ?[/math]
  1. [math]4[/math]
  2. [math]1/4[/math]
  3. [math]1/2[/math]
  4. [math]2[/math]
7. 
If [math]-a \ vec{v} = <<-9,12>>[/math] and [math]a \ vec{v} = <<9,-12>>[/math], and [math]a[/math] can be any real number (positive or negative), which of the following are possible values of [math]vec{v} ? [/math] Choose all that apply.
  1. [math]<<9,12>>[/math]
  2. [math]<<3,-4>>[/math]
  3. [math]<<-3,-4>>[/math]
  4. [math]<<-9,12>>[/math]
8. 
If [math]vec{u}[/math] has its initial point at the origin, and its terminal point at [math](3,4)[/math], where will its terminal point be if [math]vec{u}[/math] is multiplied by -2 ? Assume that its initial point remains at the origin.
  1. [math](6,8)[/math]
  2. [math](-6,8)[/math]
  3. [math](6,-8)[/math]
  4. [math](-6,-8)[/math]
9. 
Draw the vector [math]vec{v} = <<-2,-4>>[/math] with its initial point at the origin. Then, draw [math]-1/2 vec{v}[/math], also with its initial point at the origin.
Coordinate Plane - 5x5 -  Blank
  • See graph. First vector should terminate at [math](-2,-4)[/math], second vector should terminate at [math](1,2)[/math].
10. 
Draw the vector [math]vec{u} = <<3,-2>>[/math] with its initial point at the origin. Then, draw [math]3vec{u}[/math] also with its initial point at the origin.
Coordinate Plane - 10x10 - Blank
  • See graph. Vectors will be overlapping. [math]vec{u}[/math] should terminate at [math](3,-2)[/math], and [math]3vec{u}[/math] should terminate at [math](9,-6)[/math].

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