(i) Explain why two non-zero vectors in three-dimensional space are parallel if and only if one is a scalar multiple of the other, and show how this criterion is equivalent to the condition that their vector (cross) product is the zero vector.
(a) Explain the equivalence of the scalar–multiple test and the zero cross-product test for parallelism of two non-zero vectors.
(b) Using the vectors a=3i^+6j^−9k^ and b=−2i^−4j^+6k^:
(a) Show that one vector is a scalar multiple of the other.
(b) Compute a×b and state the result.