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Back to Exercise: Multiply a vector by a scalar

Exercises: Multiply a Vector by a Scalar

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Grade 9·19 problems·~28 min·Common Core Math - HS Number and Quantity·standard·hsn-vm-b-5
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A

Recall / Warm-Up

1

Vector v=⟨4,−3⟩\mathbf{v} = \langle 4, -3 \rangle. Which describes 2v2\mathbf{v} graphically?

2

Compute −3⟨2,−5⟩-3 \langle 2, -5 \rangle. What is the yy-component of the result?

3

If ∥v∥=6\|\mathbf{v}\| = 6 and c=−4c = -4, which expression gives ∥cv∥\|c\mathbf{v}\|?

B

Fluency Practice

1

Which scalar multiple of v\mathbf{v} produces a vector pointing in the OPPOSITE direction from v\mathbf{v}?

2

Let v=⟨3,−4⟩\mathbf{v} = \langle 3, -4 \rangle. Compute the xx-component of −2v-2\mathbf{v}.

3

Let v=⟨−1,6⟩\mathbf{v} = \langle -1, 6 \rangle. Compute the yy-component of 12v\frac{1}{2}\mathbf{v}.

4

Let v=⟨3,4⟩\mathbf{v} = \langle 3, 4 \rangle and c=−3c = -3. Find ∥cv∥\|c\mathbf{v}\|.

5

Let v=⟨3,4⟩\mathbf{v} = \langle 3, 4 \rangle. Find the xx-component of the unit vector v^\hat{\mathbf{v}} in the direction of v\mathbf{v}.

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