4. Use a specific example to explore how the cross product behaves under scalar multiplication. Is it true that k(a x b) = (ka ) x b = a x (kb )? Expand to the general case to prove your theory. 5. Verify (a + b) x (a + b) = ->. What can be said about two vectors whose cross product is the zero vector? 6. a) Let a = (3, 4, 1), b = (5, -2, 3) and ~ = (0, 1, -3). Find the triple product, a . ( b x c ). b) Explain why (a . b ) x ~ does not exist