# 12-4 - Solutions to Homework Assignment 4 MATH 249-01...

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Unformatted text preview: Solutions to Homework Assignment 4 MATH 249-01 and -02 Section 12.4, Page 820 1-7, 9-12, 14, 15, 25, 26, 30, 31, 34, 35, 36, 45 4. < 1 ,- 1 , 1 > × < 1 , 1 , 1 > = <- 1(1)- (1)(1) ,- [1(1)- 1(1)] , 1(1)- (- 1)(1) > = <- 2 , , 2 > . You can check the orthogonality. 6. < 1 , e t , e- t > × < 2 , e t ,- e- t > = < e t (- e- t )- e- t ( e t ) ,- [1(- e- t )- e- t (2)] , 1( e t )- e t (2) > = <- 2 , 3 e- t ,- e t > . 9. Only (a), (c), and (f) are meaningful. The others are all attempting to take a cross product in which at least one factor is a scalar. 10. | u × v | = 5 · 10 sin(60 ◦ ) = 25 √ 3 . According to the right-hand rule, it will be directed into the page. 12. (a) Since the z-axis is perpendicular to the xy-plane, we have | a × b | = 3(2) sin(90) = 6 . (b) The cross product is in the xy-plane, so the z-component is 0. It is also going to be in the second quadrant (using the right-hand rule), so its x-component is positive and its y-component is negative....
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