Hw12-2 - -6 2 2 2 = √ 49 = 7 3 ~ i-6 ~ j 2 ~ k = 7 ± 3 7...

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Mathematics 1920 Assignment 1 Section 12.2 6. (a) - 2 u = h- 2(3) , - 2(2) i = h- 6 , 4 i 5 v = h 5( - 2) , 5(5) i = h- 10 , 25 i - 2 u + 5 v = h 6 , 4 i + h- 10 , 25 i = h- 16 , 29 i (b) p ( - 16) 2 + 29 2 = 1097 12. ~ AB = h 2 - 1 , 0 - ( - 1) i = h 1 , 1 i ~ CD = h- 2 - ( - 1) , 2 - 3 i = h- 1 , - 1 i ~ AB + ~ CD = h 0 , 0 i 16. This is the unit vector which makes an angles of 135 with the positive x-axis; h cos 135 ,sin 135 i = D - 1 2 , 1 2 E 20. ~ AB = ( - 1 - 1) ~ i + (4 - 0) ~ j + (5 - 3) ~ k = - 2 ~ i + 4 ~ j + 2 ~ k 30. length = ± ± ± 1 3 ~ i + 1 3 ~ j + 1 3 ~ k ± ± ± = r 3 ² 1 3 ³ 2 = 1, the direction is 1 3 ~ i + 1 3 ~ j + 1 3 ~ k = 1 3 ~ i + 1 3 ~ j + 1 3 ~ k = 1 ² 1 3 ~ i + 1 3 ~ j + 1 3 ~ k ³ 36. (a) ~ P 1 P 2 = h 4 - 1 , - 2 - 4 , 7 - 5 i = h 3 , - 6 , 2 i ± ± ± ~ P 1 P 2 ± ± ± = p 3 2
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Unformatted text preview: + (-6) 2 + 2 2 = √ 49 = 7 3 ~ i-6 ~ j + 2 ~ k = 7 ± 3 7 ~ i-6 7 ~ j + 2 7 ~ k ² = ⇒ the direction is 3 7 ~ i-6 7 ~ j + 2 7 ~ k (b) Midpoint is ( 5 2 , 1 , 6 ) 43. 25 ◦ west of north is 90 ◦ +25 ◦ = 115 ◦ north of east. 800 h cos 115 ◦ ,sin 115 ◦ i ≈ h-338 . 095 , 725 . 046 i...
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Hw12-2 - -6 2 2 2 = √ 49 = 7 3 ~ i-6 ~ j 2 ~ k = 7 ± 3 7...

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