i have to calculate the angle between v and w. v= (1, 3, 7) w= -3x+2y+2z so w= (-3, 2, 2). so how do i find the angle between these two guys?

Question

anonymous · Answer

by the way, these are vectors we're working with here.

zarkon · Answer

$$v\cdot w=||{v}||\,||w||\cos(\theta)$$

anonymous · Answer

their lengths are IIvII=root 59 and IIwII=root 17, but i get lost after that part

zarkon · Answer

can you get 

$$v\cdot w$$?

anonymous · Answer

argh. if i multiply them together its root 1003, but that makes me feel like i did something wrong. maybe the lengths i calculated were wrong..

zarkon · Answer

dot product...you should get 17

zarkon · Answer

$$1*(-3)+3*2+7*2$$

anonymous · Answer

i did cross product, idk why. okay so when you get 17, what do you do next?

zarkon · Answer

plug in all the info into the equation I gave above...solve for $$\theta$$

zarkon · Answer

$$\theta=\cos^{-1}\left(\frac{v\cdot w}{\|v\| \|w\|}\right)$$

anonymous · Answer

θ=cos−1(17/root59 root17) woo hoo! is that good?

zarkon · Answer

yes...which is about 1.004 radians

or 57.535 deg

anonymous · Answer

you're the best zarkon!

zarkon · Answer

don't feed my ego ;)