If A = (2,-2,1) and B = (2, 0, -1)
show by explicit calculation that
i) A^B is orthogonal to A
ii) (A^B)^B lies in the same plane as A and B by expressing it as a linear combination of A and B
A^B = |A||B|sin θ
The Attempt at a Solution
I know that when you do the cross product of two vectors the result will be a vector that is perpendicular to both and I can draw a diagram to demonstrate. However I can't show it by explicit calculation. :(
I thought maybe if I could prove that the angle between them was ∏/2...