Explanation Concept Used: 1. 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 ) 2. , a → × a → = 0 3. If a → ∥ b → , then a → × b → = 0

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

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

Publisher: Kendall Hunt Publishing

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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 9.4, Problem 60PS

To determine

To prove: that if vectors OP, OQ, OR and OS lies on the same plane then, (OP×OQ)×(OR×OS)=0 .

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Chapter 9.4, Problem 59PS

Chapter 9.5, Problem 1PS

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Chapter 9 Solutions

Student's Solution and Survival Manual for Calculus

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To prove: that if vectors O P , O Q , O R a n d O S lies on the same plane then, ( O P × O Q ) × ( O R × O S ) = 0 .

Solution Summary: The author explains that the cross product of two vectors stackrelto is a vector defined by:

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To prove: that if vectors OP, OQ, OR and OS lies on the same plane then, (OP×OQ)×(OR×OS)=0 .

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Chapter 9 Solutions