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42. Suppose a and b are vectors such that a x b (3, 1, 4). What is the cross product of twice of a v b? a. (3, 1, 4) b. (6, 2, 8) c. (12, 4, 16) d. (0, 0, 0) 43. If ABC is a triangle with vertices A(2, 1, 4), B(2, 0, 1), and C(3, 0, 2), then what is AB × BC ? a. (2, 8, -3) b. (-2, -8, 3) c. (1, 3, –1) d. (-1,-3, 1) 44. What is the area of the parallelogram formed by the vectors a = (1, 0, 2) and b = (0, -1, 2)? 3 3 с. a.

42. Suppose a and b are vectors such that a x b (3, 1, 4). What is the cross product of twice of a v b? a. (3, 1, 4) b. (6, 2, 8) c. (12, 4, 16) d. (0, 0, 0) 43. If ABC is a triangle with vertices A(2, 1, 4), B(2, 0, 1), and C(3, 0, 2), then what is AB × BC ? a. (2, 8, -3) b. (-2, -8, 3) c. (1, 3, –1) d. (-1,-3, 1) 44. What is the area of the parallelogram formed by the vectors a = (1, 0, 2) and b = (0, -1, 2)? 3 3 с. a.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I need the answer for 42,43,44,45,46,47,48,49 step by step if possible 

42. Suppose a and b are vectors such that a x b = (3, 1, 4). What is the cross product of twice of a with twice of b ? (3, 1, 4) b. (6, 2, 8) (12, 4, 16) d. (0, 0, 0) a. с. 43. If ABC is a triangle with vertices A(2, 1, 4), B(2, 0, 1), and C(3, 0, 2), then what is AB × BC ? (2, 8, -3) b. (-2, -8, 3) (1, 3, -1) d. (-1, -3, 1) a. с. 44. What is the area of the parallelogram formed by the vectors a = (1, 0, 2) and b = (0, -1, 2)? a. 3 c. 2 b. 9 d. 45. A bolt is being loosened by a 40 cm wrench. The torque in this situation has a magnitude of 12 J and the force makes an angle of 60° with the wrench. What is the magnitude of the force used to loosen the bolt? 2.4 N a. с. 34.6 N b. 4.2 N d. 60.0 N 46. Determine the equation of the line through the origin and the point P( 10,3). 7 = s(10,3), s r =s(-3,10), s e R $(3,10), s 47. Determine the vector and parametric equations for the line passing through the points P(-1,-3) and Q(3,5). а. c. b. x = 3t, y = 10t, t e R d. ,SE R = 7= (3,5) +s(1,2), s x = 21 – 1, y = 41 – 3, t e R 7= (1,0) +s(2,4), s x = 1-1, y = 21 – 3, t e R SE R SER а. с. 3 (1,-3) +s(4,8), - x = 41 – 1, y = 8t – 3, t e R b. r = SER d. all of the above 48. Determine the point of intersection of the lines L,: r = (1,3,7) + s(1,2,-2), s e R and L,: = (0,2,-3) +1(1,1,4), 1 e R. P(1,3,1) b. P(1,3,7) y C. The lines coincide. a. d. no point of intersection x+2 y-3 z-2 49. Determine the parametric equation of the plane that contains the line 5 and the point 2 %3D %3D 3 P(2,5,3). a. x = 2+ 5s + 4t, y = 5 + 3s + 2t, z = 3 + 2s + t, s,t e R b. x = 2+ 5s + 3t, y = 5 +3s + 2t, z = 4 + 2s + t, s,t e R c. x = -2+5s +2t, y = 3+3s + 5t, z = 2+ 2s + 3t, s,t e R d. x = 5+2s + 2t, y = 3– 3s + 5t, z = 2 – 2s + 3t, s,t e R
Transcribed Image Text:42. Suppose a and b are vectors such that a x b = (3, 1, 4). What is the cross product of twice of a with twice of b ? (3, 1, 4) b. (6, 2, 8) (12, 4, 16) d. (0, 0, 0) a. с. 43. If ABC is a triangle with vertices A(2, 1, 4), B(2, 0, 1), and C(3, 0, 2), then what is AB × BC ? (2, 8, -3) b. (-2, -8, 3) (1, 3, -1) d. (-1, -3, 1) a. с. 44. What is the area of the parallelogram formed by the vectors a = (1, 0, 2) and b = (0, -1, 2)? a. 3 c. 2 b. 9 d. 45. A bolt is being loosened by a 40 cm wrench. The torque in this situation has a magnitude of 12 J and the force makes an angle of 60° with the wrench. What is the magnitude of the force used to loosen the bolt? 2.4 N a. с. 34.6 N b. 4.2 N d. 60.0 N 46. Determine the equation of the line through the origin and the point P( 10,3). 7 = s(10,3), s r =s(-3,10), s e R $(3,10), s 47. Determine the vector and parametric equations for the line passing through the points P(-1,-3) and Q(3,5). а. c. b. x = 3t, y = 10t, t e R d. ,SE R = 7= (3,5) +s(1,2), s x = 21 – 1, y = 41 – 3, t e R 7= (1,0) +s(2,4), s x = 1-1, y = 21 – 3, t e R SE R SER а. с. 3 (1,-3) +s(4,8), - x = 41 – 1, y = 8t – 3, t e R b. r = SER d. all of the above 48. Determine the point of intersection of the lines L,: r = (1,3,7) + s(1,2,-2), s e R and L,: = (0,2,-3) +1(1,1,4), 1 e R. P(1,3,1) b. P(1,3,7) y C. The lines coincide. a. d. no point of intersection x+2 y-3 z-2 49. Determine the parametric equation of the plane that contains the line 5 and the point 2 %3D %3D 3 P(2,5,3). a. x = 2+ 5s + 4t, y = 5 + 3s + 2t, z = 3 + 2s + t, s,t e R b. x = 2+ 5s + 3t, y = 5 +3s + 2t, z = 4 + 2s + t, s,t e R c. x = -2+5s +2t, y = 3+3s + 5t, z = 2+ 2s + 3t, s,t e R d. x = 5+2s + 2t, y = 3– 3s + 5t, z = 2 – 2s + 3t, s,t e R
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