Problem Set Complete the following assignment for a homework check and submit your work to the dropbox. 1. a) Explain wh

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Problem Set Complete The Following Assignment For A Homework Check And Submit Your Work To The Dropbox 1 A Explain Wh 1 (55.89 KiB) Viewed 49 times

Problem Set Complete the following assignment for a homework check and submit your work to the dropbox. 1. a) Explain why it is not possible for a (b) to equal (ab) (This means that the dot product is not associative.) b) Verify using an example that a +(52) 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(x) is not equal to (a*b)x č. 3. Verify using a specific example that (a + b)(a - b)=2(bxa). 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( à xôi (Kải bà (KB)? 5. Verify (a + b)(a + b)= 0. What can be said about two vectors whose cross product is zero? 6. a) Let a = (3, 4, 1), 5=(5, -2, 3) and (0, 1, -3). Find the triple product, a (b ). = b) Explain why (a b) does not exist.