Question

How do you find the angle theta in vectors using dot products?

Answer 1

\[\cos \theta = \frac{u*v}{|u| |v|}\]

Answer 2

So for example, if u= <2, 1> and v=<0,-1>, how would you plug that into the formula?

Answer 3

first find dot product
---> u*v = (2*0) + (1*-1) = -1

then find magnitude of each vector
|u| = sqrt(2^2 +1^2) = sqrt(5)
|v| = 1

\[\cos \theta = \frac{-1}{\sqrt{5}}\]

Answer 4

Alright, that makes sense thank you so much!