Test Objectives
• Demonstrate the ability to find the magnitude of a vector
• Demonstrate the ability to find the direction angle of a vector
• Demonstrate the ability to write a vector in component form
Vectors Practice Test:

#1:

Instructions: Find the magnitude and direction angle.

$$a)\hspace{.1em}\overrightarrow{v}=\langle 24, 32 \rangle$$

$$b)\hspace{.1em}\overrightarrow{p}=\langle 32, -1 \rangle$$

#2:

Instructions: Find the magnitude and direction angle.

$$a)\hspace{.1em}\overrightarrow{k}=\langle 42, 44 \rangle$$

$$b)\hspace{.1em}\overrightarrow{CD}$$ $$C=(-8, 6)$$ $$D=(-4, -5)$$

#3:

Instructions: Find the magnitude and direction angle.

$$a)\hspace{.1em}\overrightarrow{PQ}$$ $$P=(1, 8)$$ $$Q=(8, -7)$$

$$b)\hspace{.1em}\overrightarrow{PQ}$$ $$P=(-3, 9)$$ $$Q=(2, 10)$$

#4:

Instructions: Write each vector in component form.

$$a)\hspace{.1em}\left| \overrightarrow{m}\right|=50, θ=342°$$

$$b)\hspace{.1em}\left| \overrightarrow{a}\right|=61, θ=120°$$

#5:

Instructions: Write each vector in component form.

$$a)\hspace{.1em}\left| \overrightarrow{n}\right|=66, θ=45°$$

$$b)\hspace{.1em}\left| \overrightarrow{m}\right|=78, θ=330°$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}\left| \overrightarrow{v}\right|=40, θ ≈ 53.13°$$

$$b)\hspace{.1em}\left| \overrightarrow{p}\right|=5\sqrt{41}, θ ≈ 358.21°$$

#2:

Solutions:

$$a)\hspace{.1em}\left| \overrightarrow{k}\right|=10 \sqrt{37}, θ ≈ 46.33°$$

$$b)\hspace{.1em}\left| \overrightarrow{CD}\right|=\sqrt{137}, θ ≈ 289.98°$$

#3:

Solutions:

$$a)\hspace{.1em}\left| \overrightarrow{PQ}\right|=\sqrt{274}, θ ≈ 295.02°$$

$$b)\hspace{.1em}\left| \overrightarrow{PQ}\right|=\sqrt{26}, θ ≈ 11.31°$$

#4:

Solutions:

$$a)\hspace{.1em}\overrightarrow{m}=\langle 47.55, -15.45 \rangle$$

$$b)\hspace{.1em}\overrightarrow{a}=\left\langle - \frac{61}{2}, \frac{61\sqrt{3}}{2}\right\rangle$$

#5:

Solutions:

$$a)\hspace{.1em}\overrightarrow{n}=\langle 33 \sqrt{2}, 33 \sqrt{2}\rangle$$

$$b)\hspace{.1em}\overrightarrow{m}=\langle 39 \sqrt{3}, -39 \rangle$$