Hello I need some help with these 6 questions. If you could please show me all your work on a separate sheet of paper with the solutions/answers that would be great!

1. a) Explain why it is not possible for a . (b . c ) to equal (a . b) . c . (This means that the dot product is not associative.) b) Verify using an example that a + (b . c ) is not equal to (a + b) . (a + c). (This means that addition does not distribute over the dot product.) Explain the problem that arises. 2. Use a specific example to prove that the cross product is also not associative. That is, use three specific vectors in 3-space to show that a x(b x c) is not equal to (a x b) x c. 3. Verify using a specific example that (a + b) x (a - b) = 2(b xa ). Expand to the general case to prove that the result is always true. 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. 0 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 c = (0, 1, -3). Find the triple product, a . (b x c). b) Explain why (a . b) x c does not exist