Two vectors are given by A = 4 î + 7 j and B = -6 î + 2 j.(a) Find A x B.(b) Find the angle between A and BPart 1 of 4 - ConceptualizeA is in the first quadrant and B is in the second quadrant of the xy plane. The cross product A x B points along the positive z axis. We estimate the magnitude of this cross product to be less than theproduct of the magnitudes of the vectors.Part 2 of 4 - CategorizeWe express the cross product A x B in determinant form and evaluate the determinant. Then we use the magnitude of the cross product AB sin 0 to find 0.The cross product of the two vectors A and B can be expressed in determinant form.îx B4(a) Evaluating the determinant gives the following. Remember to keep track of the signs!o) + 3(0 –A x B=

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Two vectors are given by A = 4 î + 7j and B - -6 i + 2j. (a) Find AxB. (b) Find the angle between A and B.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter14: Static Equilibrium, Elasticity, And Fracture

Section: Chapter Questions

Problem 8PQ

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Question

Two vectors are given by A = 4 î + 7 j and B = -6 î + 2 j.
(a) Find A x B.
(b) Find the angle between A and B
Part 1 of 4 - Conceptualize
A is in the first quadrant and B is in the second quadrant of the xy plane. The cross product A x B points along the positive z axis. We estimate the magnitude of this cross product to be less than the
product of the magnitudes of the vectors.
Part 2 of 4 - Categorize
We express the cross product A x B in determinant form and evaluate the determinant. Then we use the magnitude of the cross product AB sin 0 to find 0.
The cross product of the two vectors A and B can be expressed in determinant form.
î
x B
4
(a) Evaluating the determinant gives the following. Remember to keep track of the signs!
o) + 3(0 –
A x B
=

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