Question

Stuck on the very last part of this:
Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <10, 6>, v = <9, 5>

Answer 1

I know they are not orthogonal, but I am trying to see if they are parallel

Answer 2

\(\sf cos\theta = \dfrac{120}{\sqrt{10^2+6^2}\sqrt{9^2+5^2}}\\\dfrac{120}{\sqrt{136} \sqrt{106}}\\cos\theta = 1.909152433\\\theta=.999444907\)
I know that for them to be parallel the cosine of the angle must be between -1 and 1, so did I go 1 step to far by finding the angle?

Answer 3

@freckles

Answer 4

\[u \cdot v = |u| |v| \text{ where } \theta=0^o \text{ and so } \cos(\theta)=1 \\ \text{ or you can have } \\ u \cdot v =-1|u||v| \text{ where } \theta=180^o \text{ and so } \cos(\theta)=-1 \]

Answer 5

like if you have theta is 0 or 180 then they are parallel

Answer 6

your equation is weird to me

Answer 7

cos(theta)=a number outside the [-1,1] range?

Answer 8

let me check your work

Answer 9

you actually had
\[\cos(\theta)=.999444906979 \text{ blah blah }\]
but since we don't have cos(theta)=1 or -1 then we can determine here without going any further that the lines aren't parallel

Answer 10

http://tutorial.math.lamar.edu/Classes/CalcII/DotProduct.aspx
good examples here

Answer 11

oh, ok
thanks :)

Answer 12

I'm not sure what the current question is but this problem was cranked out by @Coolsector here:

http://openstudy.com/updates/5076b7cde4b02f109be37e88

@sleepyjess