Question

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

u = <7, 2>, v = <21, 6>

Answer 1

If you look at vector u and v you will notice they have a common factor if 3.
So u= <7,2> while v = 3<7,2>. Since these vectors pass through the same point and have same sign they must be in the same direction which mean these vectors are parallel. Vector v = 3u. Vector v is scaled by a factor of e but still has same direction. If you want to test if they were parallel if you did not know this trick then you can take the dot product of these vectors. To test for perpendicular you would take cross product.

Answer 2

e should say 3.