12-2 - ≈< 3 321 13 071> Its magnitude is...

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Solutions to Homework Assignment 2 MATH 249-01 and -02 Section 12.2, Page 805 1-4, 6, 7-25 odd, 26-29, 31-35, 37 19. | a | = 6 2 + 2 2 + 3 2 = 7 , a + b = < 6 + ( - 1) , 2 + 5 , 3 + ( - 2) > = < 5 , 7 , 1 >, a - b = < 6 - ( - 1) , 2 - 5 , 3 - ( - 2) > = < 7 , - 3 , 5 >, 2 a = < 2(6) , 2(2) , 2(3) > = < 12 , 4 , 6 >, 3 a + 4 b = < 3(6) + 4( - 1) , 3(2) + 4(5) , 3(3) + 4( - 2) > = < 14 , 26 , 1 > . 23. < 9 , - 5 > | < 9 , - 5 > | = ¿ 9 106 , - 5 106 . 25. | 8 ˆ i - ˆ j + 4 ˆ k = 64 + 1 + 16 = 9 . The desired vector is 8 9 ˆ i - 1 9 ˆ j + 4 9 ˆ k. 29. F 1 = < - 10 cos 45 , 10 sin 45 > = < - 5 2 , 5 2 >, F 2 = < 12 cos 30 , 12 sin 30 > = < 6 3 , 6 > . Thus, F 1 + F 2 = < - 5 2+6
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Unformatted text preview: ≈ < 3 . 321 , 13 . 071 > . Its magnitude is approximately √ 3 . 321 2 + 13 . 071 2 ≈ 13 . 486 . We have cos θ ≈ 3 . 321 13 . 486 , so θ ≈ 75 . 74 degrees. 34. The weight of the chain is the magnitude of the sum of the vertical components of the two forces. This is 2 | 25sin37 | ≈ 30 . 1 N....
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