Question

Can anyone help me with vectors?

Answer 1

What's the equation

Answer 2

prove that equation

Answer 3

use the dot product, as the question suggests

A • B = <ax, ay, az>•<bx,by,bz> = ax bx + ayby + az bz

Answer 4

yes but I don't know how to progress further

Answer 5

oh, and A•B = |A| |B| cos ø

Answer 6

thank you

Answer 7

Consider the unit vector \(\dfrac{v}{\|v\|}=\left(\dfrac{x}{\|v\|},\dfrac{y}{\|v\|},\dfrac{z}{\|v\|}\right)\):\[
v\cdot e_x=x=\|{v}\|\cos(\alpha)\\
\frac{x}{\|v\|}=\cos(\alpha)\\
\frac{y}{\|v\|}=\cos(\beta)\\
\frac{z}{\|v\|}=\cos(\gamma)
\]
The unit vector has norm 1, therefore \(\cos(\alpha)+\cos(\beta)+\cos(\gamma)=1\)

Answer 8

Sorry I mean \(\cos^2(\alpha)+\cos^2(\beta)+\cos^2(\gamma)=1\)

Answer 9

thank you so much!

Answer 10

probably the most clear answer I've seen in a while on this site

Answer 11

I copy that straight from my high school textbook lol.

Answer 12

lmao i've never seen a question like this nor is it in any book given/recommended