# How do I find the magnitude and direction angle of the vector #v =6i-6j#?

##### 1 Answer

The magnitude of

#### Explanation:

In this answer, we'll define the direction angle to be

Now, for a more general case, how do we find the magnitude and direction angle of the vector

As you can see, the sides with lenghts

Using these identities, we can solve for our particular case with

Now, the sine function is negative in the fourth quadrant while the cosine is positive, so we must have

**Our vector has magnitude #6sqrt2# and direction angle #-45^@#.**