Math6A-02-S17-Patel.zhuofanzhang.Homework_1_S17.pdf

Θ degrees notes the angle between two planes is

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θ = degrees. Notes: The angle between two planes is always less than or equal to 90 . If you use arccos( ) or acos( ) within WeBWorK, it will return a value in radians. Convert to degrees. Answer(s) submitted: 49.8599 (correct) Correct Answers: 49.8599338512161 10. (1 pt) Find the area of the triangle with vertices (0, 0, 0), (-2, 0, -3), and (-2, 1, -2). A = Answer(s) submitted: 17ˆ(1/2)/2 (correct) Correct Answers: 2.06155281280883 11. (1 pt) Determine whether the points lie on a straight line. Answer Yes or No . ? 1. A ( 0 , 0 , 0 ) , B ( 7 , - 2 , 1 ) , and C ( - 28 , 8 , - 4 ) . ? 2. D ( 7 , - 2 , 1 ) , E ( 8 , 0 , 4 ) , and F ( 12 , 8 , 16 ) . ? 3. G ( - 1 , 0 , 1 ) , H ( 1 , 7 , 8 ) , and I ( 2 , 21 , 22 ) . Note: You only have two attempts at this problem. Answer(s) submitted: Yes Yes No (correct) Correct Answers: Yes Yes No 12. (1 pt) Find the angle θ between the vectors a = 10 i - j - 5 k and b = 2 i + j - 8 k . Answer (in radians): θ = Answer(s) submitted: 0.885678 (correct) Correct Answers: 0.88568 13. (1 pt) Let u = < 1 , - 1 > and v = < 1 , 2 > . Then u + v = < , > , u - v = < , > , - 3 v = < , > , u · v = , and k v k = . Answer(s) submitted: 2 1 0 -3 -3 -6 -1 5ˆ0.5 (correct) Correct Answers: 2 1 0 -3 -3 -6 -1 2.23606797749979 14. (1 pt) Find the point P such that v = -→ PQ has the components h- 5 . 25 , - 6 . 75 , - 1 . 5 i . Q = ( 1 . 75 , - 1 . 75 , 1 . 5 ) P = Solution: Solution: P = Q - v = h 1 . 75 + 5 . 25 , - 1 . 75 + 6 . 75 , 1 . 5 + 1 . 5 i = ( 7 , 5 , 3 ) . Answer(s) submitted: (7,5,3) (correct) Correct Answers: (7,5,3) 15. (1 pt) If a = i + 5 j + k and b = i + 8 j + k , find a unit vector with positive first coordinate orthogonal to both a and b .
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