Question

prove that vector a•(vector a× vector b)=0

Answer 1

a.(a×b)=a.c

where c is the cross product of a and b, which is perpendicular to both a and b.

From the projection theorem, we know that

a⋅c=|a||c|cosθ

where θ is the angle between the vectors. Since the vectors are perpendicular, hence θ=π2 and cosθ=0

∴a.c=0

⟹a.(a×b)=0