Concept explainers
Which of the following statements about the relationship between the magnitude of the cross product of two vectors and the product of the magnitudes of the vectors is true? (a)
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Chapter 11 Solutions
Physics for Scientists and Engineers
- Which of the following statements is true about the relationship between the dot product of two vectors and the product of the magnitudes of the vectors? (a) AB is larger than AB. (b) AB is smaller than AB. (c) AB could be larger or smaller than AB, depending on the angle between the vectors. (d) AB could be equal to AB.arrow_forwardFor the two vectors find A − B and |A – B| component of B along A angle between A and B A × B (A − B) × (A + B)arrow_forwardFor what values of a are the vectors A = 2ai − 2j + ak and B = ai + 2aj + 2k perpendicular?arrow_forward
- Find the angle between vectors for (a) D=(-3.0i-4.0j)m and A=(-3.0i+4.0j)m and (b) D=(2.0i+4.0j+K)m and B=(-2.0i+3.0j+2.0K)m .arrow_forwardShow that when A+B=C then A2+B2+2ABcos , where is the angle between vectors A and B .arrow_forwardLet us name three perpendicular directions as right, up, and toward you as you might name them when you are facing a television screen that lies in a vertical plane. Unit vectors for these directions are r, u, and t, respectively. Consider the quantity (3u2t). (i) Is the magnitude of this vector (a) 6, (b) 3, (c) 2, or (d) 0? (ii) Is the direction of this vector (a) down, (b) toward you, (c) up, (d) away from you, or (e) left?arrow_forward
- Scalars and vectors: Vector A has a magnitude of 9.0 and Vector B has a magnitude of 3.0. If the vectors are at an angle of 30.0º, what is the magnitude of the cross product A x B? Here are the choices: 13.5 16.2 23.4 27.0arrow_forward6:16 1 B 17.4 8. Two vectors are presented by the diagram. What is the direction and magnitude of the cross product of vector A and B (A) Out of the page, 260 (B) Out of the page, 270 (C) Into the page, 150 (D) into the page, 260 (E) Into the page, 340 A 15.6 730 a d 9. The components of vector A are given as follows: Ax = 7.6 Ay = -5.8 What is the magnitude of the vector? (A) 1.8 (B) 6.8 (C) 9.6 (D) 10.6 (E) 13.4 a d. earrow_forwardGiven two vectors A= 7i + 4j − 2k, and B= 3i − 10j + 3k, calculate the angle between them, where i, j and k are unit vectors:arrow_forward
- Two vectors are given by A = 3 î + 6 ĵ and B = -1 î + ĵ. (a) Find A × B. k (b) Find the angle between A and B.arrow_forwardFor the pair of vectors A = (6.00î + 4.00j) and B = (9.00î – 6.00j) in the xy plane, determine the following. (Enter all angle answers between 0 and 180°.) (a) The scalar product A·B = (b) The angle 0 between the vectors (c) The angles a and B which are respectively the (smallest) angles between the vector A and the positive x and positive y axes a = B = (d) The angles y and 8, which are respectively the (smallest) angles between the vector B and the positive x and positive y axes 8 =arrow_forwardWhat is the magnitude of vector B⃗? What angle vector B⃗ makes above the xy-plane?arrow_forward
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