Question

Use a specific example to explore how the cross product behaves under scalar multiplication. Is it true that k (Vector a × Vector b) = (kVector a) × Vector b = Vector a × (kVector b)? Expand to the general case to prove your theory.

Answer 1

recall that the magnitude of a×b is the area of the parallelogram formed by a and b.

So, ka×kb = k(a×kb) = k^2 a×b

think of the determinant form of the calculation. multiplying the 2nd and 3rd rows by k multiplies the determinant by k^2