Find the angle?

Question

Find the angle theta (from its cosine) between v=[1, sqrt(3)] and w=[1, 0].

 

These are vectors with 1 on top, sqrt(3) on bottom. And 1 on top, 0 on bottom for w. But how do I find the angle? Please help me with steps.

Answer 1

You use the formula

 

cos θ = v•w / ([v][w])

 

where v•w is the scalar product (or dot product) of v and w, and [v] and [w] are the magnitudes (lengths) of v and w.

In your case, v•w = [1, sqrt(3)]•[1, 0] =1, [v]=2, and [w]=1, so that

 

cos θ =1/2

 

and θ =60°.