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43. If a b = √3 and a × b = (1, 2, 2), find the angle between a and b.

43. If a b = √3 and a × b = (1, 2, 2), find the angle between a and b.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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41. A wrench 30 bolt at the origin. A force is applied at the end of the wrench. Find the magnitude of the force needed to supply 100 N-m of torque to the bolt. 3,-4) 42. Let v= 5j and let u be a vector with length 3 that starts at the origin and rotates in the xy-plane. Find the maximum and minimum values of the length of the vector u X v. In what direction does u X v point? 43. If a b = √√3 and a × b = (1, 2, 2), find the angle between a and b. 44. (a) Find all vectors v such that (1, 2, 1) × v = (3, 1,-5) S (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 the points Q and R. Show that the distance d from the point P to the line Lis d = |axb ахь a where a = QR and b = QP. (b) Use the formula in part (a) to find the distance from the point P(1, 1, 1) to the line through Q(0, 6, 8) and R(-1,4,7). 46. (a) Let P be a point not on the plane that passes through the P to the points Q, R, and S. Show that the distan plane is
Transcribed Image Text:41. A wrench 30 bolt at the origin. A force is applied at the end of the wrench. Find the magnitude of the force needed to supply 100 N-m of torque to the bolt. 3,-4) 42. Let v= 5j and let u be a vector with length 3 that starts at the origin and rotates in the xy-plane. Find the maximum and minimum values of the length of the vector u X v. In what direction does u X v point? 43. If a b = √√3 and a × b = (1, 2, 2), find the angle between a and b. 44. (a) Find all vectors v such that (1, 2, 1) × v = (3, 1,-5) S (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 the points Q and R. Show that the distance d from the point P to the line Lis d = |axb ахь a where a = QR and b = QP. (b) Use the formula in part (a) to find the distance from the point P(1, 1, 1) to the line through Q(0, 6, 8) and R(-1,4,7). 46. (a) Let P be a point not on the plane that passes through the P to the points Q, R, and S. Show that the distan plane is
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