Question

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

Answer 1

@mathmale could you help after you are finished helping the other person? :)

Answer 2

take the dot product of the vectors, if the dot product = 0, then they're orthogonal

take common factor to both vectors, if the value inside is the same, then that means they're parallel, since one vector is just the other multiplied by some scalar factor

Answer 3

What course are you in? I'm used to tutoring this material for a course named "Multivariable Calculus."

You are comparing two vectors, (bold)u and (bold)v.
If it happens that both x-coordinates and both y-coordinates are related to one another by the same multiplier, then the two vectors are parallel.

Let's see whether that's the case here.
<1, -2>, v = <-4, 8> have x-comps 1 and -4. Let's say that the -4 is the result of multiplying that 1 by -4. We ask whether the larger y-comp is also -4 times -2. Is (-4)(-2)=8?

Again:

(-4)(1) = -4
and
(-4)(-2)=8

So we conclude that vectors (bold)u and (bold)v are ..... ???

Answer 4

Thank you for both of your responses! I am in Precalc. Based on your response mathmale I think that we can conclude that both vectors are parallel.

Answer 5

Can you help on another question? that was very helpful @mathmale

Answer 6

Compliments to @jdoe0001: His solution is more sophisticated than mine. Nice work!!

sure, go ahead and post another question (but separate from this one, please).

Answer 7

Alright, i might have a few more questions, im taking a practice test and don't really understand the material to well.