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.

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Chapter1: Units, Trigonometry. And Vectors
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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
=
Transcribed Image Text: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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