Exercises: Find Components of a Vector

Work through each section in order. Show your work for all computation problems. Express component vectors in angle-bracket notation.

Grade 9·20 problems·~30 min·Common Core Math - HS Number and Quantity·standard·hsn-vm-a-2

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Recall / Warm-Up

What does the component form of a vector $\langle v_x, v_y \rangle$ tell you?

The starting position of the vector in the coordinate plane.

The horizontal and vertical displacement the vector produces.

The magnitude and direction angle of the vector.

The coordinates of the terminal point of the vector.

A vector goes from point $A(1, 2)$ to point $B(5, 6)$ . Which formula correctly finds the horizontal component $v_x$ ?

$v_x = x_1 - x_2 = 1 - 5 = -4$

$v_x = x_2 - x_1 = 5 - 1 = 4$

$v_x = x_1 + x_2 = 1 + 5 = 6$

$v_x = x_2 = 5$

A vector has component form $\langle -3, 5 \rangle$ . Which description matches?

3 units right and 5 units up

3 units left and 5 units up

3 units left and 5 units down

3 units right and 5 units down

Find the component form of the vector from $A(2, 5)$ to $B(7, 9)$ . Enter the horizontal component $v_x$ .

Find the component form of the vector from $P(-1, 4)$ to $Q(3, -2)$ . Enter the vertical component $v_y$ .

The vector $\overrightarrow{CD}$ goes from $C(3, 1)$ to $D(3, 6)$ . What is its component form?

$\langle 3, 6 \rangle$

$\langle 0, 5 \rangle$

$\langle 6, 5 \rangle$

$\langle 5, 0 \rangle$

Which statement correctly interprets the component vector $\langle 4, -7 \rangle$ ?

4 units left and 7 units up

4 units right and 7 units up

4 units right and 7 units down

4 units left and 7 units down

Compute the magnitude of the vector $\langle 5, 12 \rangle$ . Enter the exact value.

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