Question

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

u = <6, -2>, v = <8, 24>

Answer 1

If they were parallel one vector would be able to match the other when multiplied by a scalar.

If they're orthogonal, this can be proved by showing that a vector orthogonal to one of them is parallel to the other.

Answer 2

This is kind of hard to explain, but let's take a vector orthogonal to u:

<-2, -6>

If you multiply this by the scalar -4, you obtain <8, 24>

This shows that u and v are orthogonal

Answer 3

If that's not clear I can try to explain further

Answer 4

I understand, so that mean it is neither

Answer 5

No, the vectors are orthogonal. You can eyeball it here:

http://www.wolframalpha.com/input/?i=6i-2j%2C+8i%2B24j

Answer 6

You can also prove it by finding the angle between the vectors

Answer 7

I see now

Answer 8

If you use

cos(theta)= (cross product of u vector and v vector) / (product of vector lengths)

and solve for theta, you should find theta = 90 degrees or pi / 2 radians, indicating the vectors are perpendicular (orthogonal)