How do I prove that A^B is orthogonal to A?

[EmmaLemming]

Homework Statement

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

Homework Equations

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...

 

[astrozilla]

If you know how to calculate cross product ^ , you will do A^B and if you find correctrly the value ~(itwill be a vector the result ,lets call it C) then you take the dot product of C with A and if it is zero they are orthogonal.

since cos90 =0 and (A) dot (B)= A B cosθ

ii)i think you can use the identity : a x ( b x c ) = b(ac) -c(ab) , b=a here