Test Objectives
  • Demonstrate the ability to find the sum of two vectors
  • Demonstrate the ability to multiply a vector by a scalar
Operations with Vectors Practice Test:

#1:

Instructions: Find the resultant using the triangle method.

$$a)\hspace{.1em}\overrightarrow{a}=\langle -5,1 \rangle, \overrightarrow{b}=\langle 6, -8 \rangle$$

Instructions: Find the resultant using the parallelogram method.

$$b)\hspace{.1em}\overrightarrow{a}=\langle 4,5 \rangle, \overrightarrow{b}=\langle 6, -8 \rangle$$


#2:

Instructions: Find the component form of the resultant vector.

$$a)\hspace{.1em}\overrightarrow{f}=\langle -3,9 \rangle, \overrightarrow{b}=\langle -7, -1 \rangle$$ $$\text{Find}: 2\overrightarrow{f}+ \hspace{.2em}6\overrightarrow{b}$$

$$b)\hspace{.1em}\overrightarrow{u}=\langle 3,-10 \rangle, \overrightarrow{b}=\langle -11, -5 \rangle$$ $$\text{Find}: 9\overrightarrow{u}+ \hspace{.2em}8\overrightarrow{b}$$


#3:

Instructions: Find the component form of the resultant vector.

$$a)\hspace{.1em}\overrightarrow{f}=\langle -5,1 \rangle, \overrightarrow{v}=\langle 2, 12 \rangle$$ $$\text{Find}: 5\overrightarrow{f}+ \hspace{.2em}5\overrightarrow{v}$$

$$b)\hspace{.1em}\overrightarrow{u}=\langle 11,6 \rangle, \overrightarrow{v}=\langle 2, -5 \rangle$$ $$\text{Find}: -4\overrightarrow{u}- \hspace{.2em}9\overrightarrow{v}$$


#4:

Instructions: Find the component form of the resultant vector.

$$a)\hspace{.1em}\overrightarrow{f}=\langle 5,-7 \rangle, \overrightarrow{g}=\langle -6, -6 \rangle$$ $$\text{Find}: -2\overrightarrow{f}- \hspace{.2em}9\overrightarrow{g}$$

$$b)\hspace{.1em}\overrightarrow{a}=\langle 12,-7 \rangle, \overrightarrow{v}=\langle 10, -8 \rangle$$ $$\text{Find}: 4\overrightarrow{a}+ \hspace{.2em}5\overrightarrow{v}$$


#5:

Instructions: Find the component form of the resultant vector.

$$a)\hspace{.1em}\left|\overrightarrow{u}\right|=10, θ=184° $$ $$\left|\overrightarrow{b}\right|=14, θ=304°$$ $$\text{Find}: -\overrightarrow{u}- \hspace{.2em}\overrightarrow{b}$$

$$b)\hspace{.1em}\left|\overrightarrow{f}\right|=12, θ=24° $$ $$\left|\overrightarrow{b}\right|=18, θ=52°$$ $$\text{Find}: 8\overrightarrow{f}- \hspace{.2em}8\overrightarrow{b}$$


Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}\overrightarrow{a}+ \overrightarrow{b}=\langle 1, -7 \rangle$$ showing the sum of vector a and b using the triangle method

$$b)\hspace{.1em}\overrightarrow{a}+ \overrightarrow{b}=\langle 10, -3 \rangle$$ showing the sum of vector a and b using the parallelogram method


#2:

Solutions:

$$a)\hspace{.1em}2\overrightarrow{f}+ 6\overrightarrow{b}=\langle -48, 12 \rangle$$

$$b)\hspace{.1em}9\overrightarrow{u}+ 8\overrightarrow{b}=\langle -61, -130 \rangle$$


#3:

Solutions:

$$a)\hspace{.1em}5\overrightarrow{f}+ 5\overrightarrow{v}=\langle -15, 65 \rangle$$

$$b)\hspace{.1em}-4\overrightarrow{u}- 9\overrightarrow{v}=\langle -62, 21 \rangle$$


#4:

Solutions:

$$a)\hspace{.1em}-2\overrightarrow{f}- 9\overrightarrow{g}=\langle 44, 68 \rangle$$

$$b)\hspace{.1em}4\overrightarrow{a}+ 5\overrightarrow{v}=\langle 98, -68 \rangle$$


#5:

Solutions:

$$a)\hspace{.1em}-\overrightarrow{u}- \overrightarrow{b}=\langle 2.15, 12.3 \rangle$$

$$b)\hspace{.1em}8\overrightarrow{f}- 8\overrightarrow{b}=\langle -0.95, -74.43 \rangle$$