37 82232. P(2, -3, 4), Q(-1, -2, 2), R(3, 1, -3)CHAPTER 12 Vectors and the Geometry of Space33-34 Find the volume of the parallelepiped determined by thevectors a, b, and c.33. a = (1, 2, 3), b = (-1, 1, 2), c = (2, 1, 4)34. a = i + j, b=j+k,c=i+j+k25035-36 Find the volume of the parallelepiped with adjacent edgesPQ, PR, and PS.35. P(-2, 1, 0),Q(2, 3, 2),36. P(3, 0, 1), Q(-1, 2, 5),37. Use the scalar triple product to verify that the vectorsu = i + 5j-2 k, v = 3i- j, and w = 5i + 9j - 4kare coplanar.The38. Use the scalar triple product to determine whether the pointsA(1, 3, 2), B(3, -1, 6), C(5, 2, 0), and D(3, 6, -4) lie in thesame plane.39. A bicycle pedal is pushed by a foot with a 60-N force asshown. The shaft of the pedal is 18 cm long. Find the magni-tude of the torque about P.2 ft0.6 ftR(1, 4, -1),R(5, 1, -1),60 NP0.6 ft70°40. (a) A horizontal force of 20 lb is applied to the handle of a Sgearshift lever as shown. Find the magnitude of the torqueabout the pivot point P.(b) Find the magnitude of the torque about P if the same forceis applied at the elbow Q of the lever.S(3, 6, 1)S(0, 4, 2)1 ft10⁰QP20 lb41. A wrench 30 cm long lies along the positive y-axis and grips abolt at the origin. A force is applied in the direction (0,3,-4)at the end of the wrench. Find the magnitude of the forceneeded to supply 100 Nm of torque to the bolt.42. Let v = 5j and let u be a vector with length 3 that starts atthe origin and rotates in the xy-plane. Find the maximum andminimum values of the length of the vector u X v. In whatdirection does u X v point?43. If a b = √3 and a × b = (1, 2, 2), find the angle between aand b.44. (a) Find all vectors v such that(1, 2, 1) × v = (3, 1,-5) EXX(b) Explain why there is no vector v such that(1, 2, 1) X v = (3, 1,5)45. (a) Let P be a point not on the line L that passes through thepoints Q and R. Show that the distance d from the point Pto the line Lisd=where a = QR and b = QP.(b) Use the formula in part (a) to find the distance fromthe point P(1, 1, 1) to the line through Q(0, 6, 8) andR(-1,4,7).46. (a) Let P be a point not on the plane that passes through thepoints Q, R, and S. Show that the distance d from P to theplane isd=axb|a52. Prove that|a (bx c) |axb|.where a = QR, b = Qs, and c =QP.(b) Use the formula in part (a) to find the distance from thepoint P(2, 1, 4) to the plane through the points Q(1, 0, 0),R(0, 2, 0), and S(0, 0, 3).47. Show that a × b ² = |a|²|b|² - (a - b)².48. If a + b + c = 0, show thataXb=bXc=cXa49. Prove that (a - b) x (a + b) = 2(a X b).50. Prove Property 6 of cross products, that is,ax (bx c) = (ac)b - (a - b)c51. Use Exercise 50 to prove thatax (bx c) + bx (cx a) + cx (ax b) = 0(a X b) (cx d)=a c b ca d b d

Name: 37 82232. P(2, -3, 4), Q(-1, -2, 2), R(3, 1, -3)CHAPTER 12 Vectors and
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Description: 37 82232. P(2, -3, 4), Q(-1, -2, 2), R(3, 1, -3)CHAPTER 12 Vectors and the Geometry of Space33-34 Find the volume of the parallelepiped determined by thevectors a, b, and c.33. a = (1, 2, 3), b = (-1, 1, 2), c = (2, 1, 4)34. a = i + j, b=j+k,c=i+j+k2

The given question is based on the basic vector components. To solve the given problem we will…

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37. Use the scalar triple product to verify that the vectors u = i + 5j - 2k, v = 3i - j, and w = 5i + 9j - 4k are coplanar.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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