Explanation Given : Point is ( − 1 , 2 , 1 ) . Plane passes through ( − 1 , 1 , 1 ) , ( 4 , 3 , 7 ) and ( 3 , − 1 , 0 ) . Calculation: For equation of plane, Let the points as P ( − 1 , 1 , 1 ) , Q ( 4 , 3 , 7 ) and R ( 3 , − 1 , 0 ) . Then the vector is PQ is calculated as follows: P Q = 〈 ( 4 − ( − 1 ) ) , ( 3 − 1 ) , ( 7 − 1 ) 〉 = 〈 5 , 2 , 6 〉 Then the vector is PR is calculated as follows: P R = 〈 ( 3 − ( − 1 ) ) , ( − 1 − 1 ) , ( 0 − 1 ) 〉 = 〈 4 , − 2 , − 1 〉 Normal vector is calculated as follows: n = P Q × P R = | i j k 5 2 6 4 − 2 − 1 | = ( −

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Question

Chapter 9.6, Problem 23PS

To determine

The distance from the point (−1,2,1) to the plane passes through (−1,1,1) , (4,3,7) and (3,−1,0) .

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Chapter 9.6, Problem 22PS

Chapter 9.6, Problem 24PS

Chapter 9 Solutions

Calculus

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The distance from the point ( − 1 , 2 , 1 ) to the plane passes through ( − 1 , 1 , 1 ) , ( 4 , 3 , 7 ) and ( 3 , − 1 , 0 ) .

Solution Summary: The author calculates the distance from the point (-1,2,1) to the plane.

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The distance from the point (−1,2,1) to the plane passes through (−1,1,1) , (4,3,7) and (3,−1,0) .

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Chapter 9 Solutions