Explanation Given: The vectors, w = 〈 1 , 0 , − 3 〉 u = 〈 6 , − 1 , 2 〉 Formula used: Vector cross product The cross product of two vectors a and b , when their magnitudes ‖ a ‖ and ‖ b ‖ and the angle between them θ are known is given by the formula, a × b = ‖ a ‖ ⋅ ‖ b ‖ ⋅ sin ( θ ) n Where n is the unit vector at right angles to both a and b The cross product of the given two vectors a = 〈 a 1 , a 2 , a 3 〉 and b = 〈 b 1 , b 2 , b 3 〉 can also be calculated using the formula below, a × b = 〈 c 1 , − c 2 , c 3 〉 where c 1 = a 2 b 3 − a 3 b 2 c 2 = a 1 b 3 − a 3 b 1 c 3 = a 1 b 2 − a 2 b 1 Considering i, j and k to be the standard unit vectors in R 3 (assuming the right handed coordinate system), we can write the cross product in the form of the determinant as follows, a × b = | i j k a i a j a k b i b j b k | The cross product of two vectors is another vector that is at right angles to both...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 13, Problem 34CRE

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To calculate:

The cross product of the given vectors

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Chapter 13, Problem 33CRE

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Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

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The cross product of the given vectors

Solution Summary: The author explains the formula used to calculate the cross product of two vectors a and b.

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Chapter 13 Solutions

To calculate:

The cross product of the given vectors