Hey guys. I'm trying to prove that u.v=|u||v|cos(theta)

please help

>>8596951
You have it backwards.

[math]cos (\theta) = adj/hyp [\math]

implies u.v is adj. And ||u|| ||v|| is the hypotenuse

>>8596991

so you're telling me that

u.v = proj (v) onto (u)

and

||u|| ||v|| = v ?? that can't be right.

i have a right triangle drawn - imagine u on the x axis and v at (1,1).

File: 20170112_151004.jpg (4MB, 5312x2988px) Image search: [Google]

4MB, 5312x2988px

THIS is what I'm trying to do

Can someone point out where I'm going wrong

Or how to continue

>>8597066

so i don't know if i'm right in using ||v|| instead of v when i re-write cosine

and i don't know what to do

someone please advise

>>8597066
>>8597077
>mgw covered this last lecture but can't help you excactly out


IIvII is just the length thus when you multiplicate a vector x with itself you get the actual length. https://en.wikipedia.org/wiki/Euclidean_norm

So when you want to measure the angle of 2 vectors you just gotta calculate a*b = IIaII * IIbII * (cos alpha sin alpha) * (cos beta sin beta).

other than thatyou can use the basis-vectors. But that's some insight that might help you maybe to get you going

isn't this sort of equivalent to proving the law of cosines?

>>8597096
>>8597088
>88▶
>>>8597066
>>>8597077 (You)
>>mgw covered this last lecture but can't help you excactly out
>IIvII is just the length thus when you multiplicat

Yes but I'm trying to solve this without using the law of cosines, but using some sort of algebraic manipulation instead.

>>8596951
Brainlet here.
what's the whole double bracketing for? Is that a double absolute value or something?

>>8597111

it means the magnitude or length of a vector

>>8596951
why not just pick a coordinate system where u_vec = (u,0,0). so u . v = u*v_1 and v_1 = ||v|| cos theta from the definition of cos.