MA330: Assignment 1
Required Reading.
• Read Chapter 1, § 1-4, 9-13
To be turned in March 15th at the start of class.
1. Textbook, page 6, # 1
2. Textbook, page 10, #1
3. Textbook, page 29, #1ae
4. Textbook, page 29, #3
5. Textbook, page 29, #4
6. Textbook, page 34, #1b
7. Textbook, page 34, #2ac
8. Using only formulas from class, prove the following.
(a + b) × (c + d) = a × c + a × d + b × c + b × d
9. The following formula can be found in §12 of the textbook.
(u × v) × w = (u · w)v − (v · w)u
Use it to prove that
(a × b) × c − a × (b × c) = (a · b)c − (b · c)a
10. Assume {a, b, c} are all non zero vectors. Use the result of the previous problem to prove that
(a × b) × c = a × (b × c) only if c is parallel to a or b is orthogonal to both a and c.
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