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

Question

Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <1, -2>, v = <-4, 8>

e.mccormick · Answer

I would start with the dot product.  If it is 0, then they are orthogonal, and it is easy to do.

anonymous · Answer

(1)(-4) + (-2)(8) = -4 + (-16) = -20

e.mccormick · Answer

So that eliminates that right off.

anonymous · Answer

OKay so it can be parallel or neither

e.mccormick · Answer

Next, would be to look and see if they are parallel.

e.mccormick · Answer

If you can multiply by some scalar on one vector and get the other, they are parallel.

e.mccormick · Answer

So, can you find a c such that $c\vec{u}=\vec{v}$

anonymous · Answer

Idk what that means lol... what do i do?

amistre64 · Answer

just stack the vectors, if they result in a common ratio they are paraleel

e.mccormick · Answer

Ah, do you know what scalar multiplication of a vector is?  If not, I can show that real fast.

amistre64 · Answer

u = <1, -2> v = <-4, 8> -1/4 = -2/8

e.mccormick · Answer

@amistre64 Ah, that is a nice test for it.

anonymous · Answer

So since they are a common ratio then that means they are parallel right?

amistre64 · Answer

correct

anonymous · Answer

Thanks guys! how do i give a medal to both of you?

amistre64 · Answer

i have enough medals :)

anonymous · Answer

Oh true lol

e.mccormick · Answer

That can also be seen with $-4\vec{u}=\vec{v}$ but that method is much nicer!

anonymous · Answer

Thanks again guys

e.mccormick · Answer

np.  Have fun!