Explanation Given information : The requiredvector is determined by the line of intersections of the planes x + y + z =3 and 2 x + 3 y − z =4 . Formula used : The line of intersections of two planes is determined bythe vector N 1 → × N 2 → , where N 1 → and N 2 → are vectors normal to the planes. The line of intersection of planes is parallel to the vector N 1 → × N 2 → . Calculations: The given planesare x + y + z =3 … (1) 2 x + 3 y − z =4 … (2) The vectors normal to the planes (1) and (2) are N 1 → =i+j+k , and N 2 → =2i+3j-k respectively. The vector perpendicular to both normals N 1 → and N 2 → is N 1 → × N 2 → = | i j k 1 1 1 2 3 -1 | =- 4i+3j+k

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Vector Calculus

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Question

Chapter 9.6, Problem 45PS

To determine

Tofind:The direction cosines of avector determined by the line of intersection of two plane.

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Chapter 9.6, Problem 44PS

Chapter 9.6, Problem 46PS

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Chapter 9 Solutions

Calculus

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Tofind: The direction cosines of avector determined by the line of intersection of two plane.

Solution Summary: The author explains the direction cosines of avector determined by the line of intersection of two planes.

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Tofind:The direction cosines of avector determined by the line of intersection of two plane.

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Chapter 9 Solutions