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Common Core Standard HSN-VM.B.5b Questions

Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).

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Grade 11 Vectors CCSS: HSN-VM.B.5, HSN-VM.B.5b
For [math]vec{v} = <<-4,2>>[/math], find [math]||3vec{v}||[/math].
  1. [math]6[/math]
  2. [math]2sqrt(5)[/math]
  3. [math]6sqrt(5)[/math]
  4. [math]60[/math]
Grade 11 Vectors CCSS: HSN-VM.B.5, HSN-VM.B.5b
If [math]||5vec{u}|| = 15[/math], what is the value of [math]||vec{u}|| ?[/math]
  1. 3
  2. 5
  3. 10
  4. Not enough information to determine.
Grade 11 Vectors CCSS: HSN-VM.B.5, HSN-VM.B.5b
For vectors [math]vec{n} = 6vec{v}[/math] and [math]vec{m} = -12vec{v}[/math], which of the following statements are correct? Choose all correct answers.
  1. The vectors have opposite directions.
  2. [math]-2||vec{n}|| = ||vec{m}||[/math]
  3. Both vectors are in the same direction as [math]vec{v}[/math].
  4. The magnitude of [math]vec{m}[/math] is twice that of [math]vec{n}[/math].
Grade 11 Vectors CCSS: HSN-VM.B.5, HSN-VM.B.5b
For [math]vec{v} = <<3,2>>[/math], find [math]|| -10vec{v}||[/math].
  1. [math] -10sqrt{13}[/math]
  2. [math]sqrt{130}[/math]
  3. [math]50[/math]
  4. [math]10sqrt{13}[/math]
Grade 11 Vectors CCSS: HSN-VM.B.5, HSN-VM.B.5b
If you are given [math]vec{v}[/math], which of the following is a vector that is twice as long but in the opposite direction?
  1. [math]2vec{v}[/math]
  2. [math]-2vec{v}[/math]
  3. [math]1/2 vec{v}[/math]
  4. [math]-1/2 vec{v}[/math]
Grade 11 Vectors CCSS: HSN-VM.B.5, HSN-VM.B.5b
For a given vector, [math]vec{v}[/math], and scalar multiple [math]a, \ a<0[/math], which of the following statements is correct?
  1. The direction of [math]a \ vec{v}[/math] is the same as the direction of [math]vec{v}[/math].
  2. The direction of [math]a \ vec{v}[/math] is opposite to that of [math]vec{v}[/math].
  3. The direction of the two vectors is different, but it is impossible to tell how they are different.
  4. The direction of the two vectors is different, but the difference will be less than 180°.
Grade 11 Vectors CCSS: HSN-VM.B.5, HSN-VM.B.5b
Which of the following statements is true if [math]vec{v}[/math] is a non-zero vector, [math]a[/math] is a scalar such that [math]a< -1[/math], and [math]vec{w} = a vec{v} ?[/math]
  1. [math]||vec{w}|| = ||a vec{v}||[/math]
  2. [math]||vec{w}|| < ||a vec{v} || [/math]
  3. [math]||vec{w}|| > ||a vec{v} || [/math]
  4. [math] || vec{w}|| = - || vec{v}||[/math]
Grade 11 Vectors CCSS: HSN-VM.B.5, HSN-VM.B.5b
For the vectors [math]vec{n}[/math] and [math]vec{m}[/math], [math]||a \ vec{n}|| = ||vec{m}||[/math] for scalar [math]a[/math], where [math]a[/math] can be any non-zero real number. Which of the following statements must be true?
  1. The two vectors have the same direction.
  2. The two vectors have the opposite direction.
  3. The ratio of the magnitudes of [math]vec{m}[/math] to [math]vec{n}[/math] is [math]a[/math] to [math]1[/math].
  4. The two vectors are equal.
Grade 11 Vectors CCSS: HSN-VM.B.5b
The vectors [math]4vec(n)[/math] and [math]-4vec(n)[/math]
  1. have nothing in common.
  2. have the opposite direction.
  3. have the same direction.
  4. have the opposite magnitude.
Grade 11 Vectors CCSS: HSN-VM.B.5, HSN-VM.B.5b
The vectors [math]4vec(n)[/math] and [math]6vec(n)[/math]
  1. have nothing in common.
  2. have the same direction.
  3. have the same start point.
  4. have the same magnitude.

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