Question

Find the direction angle of v for each vector.

$v=-i+3j$

Short answer

The angle of v is $108.5^o$.

Step-by-step solution

Step 1. Given information  

We have been given a vector $v=-i+3j$.

We have to find its direction.

Step 2. Write the formula 

The angle between the vector and complex axisi is given as

$\alpha ={\tan }^{-1}\frac{b}{a}$

Step 3. Substitute the values 

$$\begin{gathered} \alpha ={\tan }^{-1}\frac{3}{-1} \\ \alpha ={\tan }^{-1}-3 \\ \alpha =-71.5^o \end{gathered}$$

Since the vector is located in the second quadrant, the angle will be $108.5^o$.