Exercises: Multiply a Vector by a Scalar

Work through each section in order. Show your work where indicated.

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

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Recall / Warm-Up

Vector $\mathbf{v} = \langle 4, -3 \rangle$ . Which describes $2\mathbf{v}$ graphically?

An arrow twice as long as $\mathbf{v}$ , pointing in the same direction

An arrow twice as long as $\mathbf{v}$ , pointing in the opposite direction

An arrow rotated $90\degree$ from $\mathbf{v}$

An arrow with the same length as $\mathbf{v}$ but moved 2 units right

Compute $-3 \langle 2, -5 \rangle$ . What is the $y$ -component of the result?

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

$|-4| \cdot 6 = 24$

$-4 \cdot 6 = -24$

$(-4)^2 \cdot 6 = 96$

$6 - 4 = 2$

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

$3\mathbf{v}$

$-2\mathbf{v}$

$\frac{1}{2}\mathbf{v}$

$1 \cdot \mathbf{v}$

Let $\mathbf{v} = \langle 3, -4 \rangle$ . Compute the $x$ -component of $-2\mathbf{v}$ .

Let $\mathbf{v} = \langle -1, 6 \rangle$ . Compute the $y$ -component of $\frac{1}{2}\mathbf{v}$ .

Let $\mathbf{v} = \langle 3, 4 \rangle$ and $c = -3$ . Find $\|c\mathbf{v}\|$ .

Let $\mathbf{v} = \langle 3, 4 \rangle$ . Find the $x$ -component of the unit vector $\hat{\mathbf{v}}$ in the direction of $\mathbf{v}$ .

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