Explanation Concept Used: Cross product ( vector product ) of two vectors a = { a x ; a y ; a z } and b = { b x ; b y ; b z } in Cartesian coordinate system is a vector defined by: a ¯ × b ¯ = | i j k a x a y a z b x b y b z | = i ( a y b z − a z b y ) − j ( a x b z − a z b x ) + k ( a x b y − a y b x ) The following three vectors are given: u = i + j , v = 2 i − j + k w = − 3 i Here, u × v = | i j k 1 1 0 2 − 1 1 | = i ( 1 ⋅ 1 − 0 ⋅ ( − 1 ) ) − j ( 1 ⋅ 1 − 0 ⋅ 2 ) + k ( 1 ⋅ ( − 1 ) − 1 ⋅ 2 ) = i ( 1 − 0 ) − j ( 1 − 0 ) + k ( − 1 − 2 ) = { 1 , − 1 , − 3 } Thus, ( u × v ) × w = | i j k 1 − 1 − 3 − 3 0 0 | = i ( ( − 1 ) ⋅ 0 − ( − 3 ) ⋅ 0 ) − j ( 1 ⋅ 0 − ( − 3 ) ⋅ ( − 3

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Question

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 9.4, Problem 39PS

To determine

To find: the value of (u×v)×w and u×(v×w) for the given vectors.

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Chapter 9.4, Problem 38PS

Chapter 9.4, Problem 40PS

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Chapter 9 Solutions

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the value of ( u × v ) × w a n d u × ( v × w ) for the given vectors .

Solution Summary: The author explains that the cross product of three (or any number of vectors) is not associative in general.

Concept explainers

To find: the value of (u×v)×w and u×(v×w) for the given vectors.

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Chapter 9 Solutions