How do you solve these?

1. a) Verify using an example that a . (b . c ) = (a . b) . c is not true. Explain your reasoning both numerically and by using the definition of the dot product. b) Verify using an example that a + (b . c ) # (a . b) + ? Explain your reasoning. 2. Use a specific example then expand to the general case to determine if the cross product has the associative property. That is, determine if a x (b x c) =(a x b) x C? 3. Verify using an example that (a + b) x (a - b) = 2(a x b). Use a specific example then expand to the general case to determine if the cross product has the distributive property. 4. Use a specific example then expand to the general case to determine what happens under scalar multiplication. That is, determine if k(a x b) = (ka ) x b = a x (kb)? 5. Verify (a + b) x (a + b) = 0. What can be said about two vectors whose cross product is zero? 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 c does not exist