math! vectors?

Question

Use the Law of Cosines to find the angle between the given vectors. Assume angle is greater than or equal to 0, less than or equal to 180

v= i+j
w=2(i-j)

Answer 1

v = <1,1>
w = <2,-2>

if you think about it graphically, v is 45° above x axis, w is 45° below, so angle between should be 90°, but let's do it the hard way.

cos A = v•w / ||v||•||w||
cos A = (1•2 + 1•-2) / (√2)(2√2)
cos A = 0/4 = 0
so A is 90°

that's not quite law of cosines for triangles, but to get the angle that way we'd have had to use the distance formula to get the 3rd side of the triangle.

Answer 2

v is at 45°
w is at - 45°
Angle between v and w = 90°