# How do you determine whether u and v are orthogonal, parallel or neither given #u=<3, 15># and #v=<-1, 5>#?

##### 2 Answers

Please see the explanation.

#### Explanation:

Compute the dot-product:

The two vectors are not orthogonal; we know this, because orthogonal vectors have a dot-product that is equal to zero.

Determine whether the two vectors are parallel by finding the angle between them.

Compute the magnitude of both vectors:

The angle between them is:

If they were parallel the angle would be

The answer is neither.

The vectors are not parallel and not orthogonal.

#### Explanation:

To see if 2 vectors, we do a dot product

As the dot product is

If 2 vectors are parallel,

then,

Therefore,

This is not possible, so the vectors are not parallel