How do you determine whether u and v are orthogonal, parallel or neither given #u=<3, 15># and #v=<-1, 5>#?
Please see the 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.
To see if 2 vectors, we do a dot product
As the dot product is
If 2 vectors are parallel,
This is not possible, so the vectors are not parallel