Question

Determine whether u and v are orthogonal, parallel, or neither.

u = 1/4 (3i - j)       v = 5i + 6j

Answer 1

Step 1:

The vectors  and

Rewrite the vectors as and

The vectors are orthogonal If

The dot product of the vectors and is defined as .

Since the dot product is not equals to zero, the vectors are not orthogonal.

Step 2:

The dot product of the vectors is .

The vectors are parallel then angle between the vectors is zero.

The magnitude of vector :

The magnitude of vector :

The vectors are not parallel to each other.

Solution:

The vectors are neither orthogonal nor parallel.