Explanation Given information: Points ( 0 , 2 , − 1 ) , ( 1 , − 3 , 5 ) & ( 3 , 0 , − 2 ) Concept and Formula Used: The normal to the plane is given by N = P R × P Q . Equation of plane with normal N = A i +B j +C k and contain the points ( x 0 , y 0 , z 0 ) is given by A ( x − x 0 ) + B ( y − y 0 ) + C ( z − z 0 ) = 0 Cross product of vectors. Calculation: The plane is passing through the points P ( 0 , 2 , − 1 ) ,Q ( 1 , − 3 , 5 ) &R ( 3 , 0 , − 2 ) , therefore the normal to the plane is given by N = P R × P Q P R =PV of R − PV of P P ( 0 , 2 , − 1 ) ,Q ( 1 , − 3 , 5 ) &R ( 3 , 0 , − 2 ) P R = ( 3 − 0 ) i + ( 0 − 2 ) j + ( − 2 + 1 ) k = 3 i − 2 j − 1 k P Q = PV of Q − PV of P P ( 0 , 2 , − 1 ) ,Q ( 1 , − 3 , 5 ) &R ( 3 , 0 , − 2 ) P Q =</

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 9, Problem 21PE

To determine

To Calculate: The equation of plane passing through three points (0,2,−1),(1,−3,5)&(3,0,−2)

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Chapter 9, Problem 20PE

Chapter 9, Problem 22PE

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Chapter 9 Solutions

Calculus

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The equation of plane passing through three points ( 0 , 2 , − 1 ) , ( 1 , − 3 , 5 ) & ( 3 , 0 , − 2 )

Solution Summary: The author calculates the equation of plane passing through three points. The normal to the plane is given by N=PRtimes PQ.

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To Calculate: The equation of plane passing through three points (0,2,−1),(1,−3,5)&(3,0,−2)

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Chapter 9 Solutions

The equation of plane passing through three points ( 0 , 2 , − 1 ) , ( 1 , − 3 , 5 ) &amp; ( 3 , 0 , − 2 )

Solution Summary: The author calculates the equation of plane passing through three points. The normal to the plane is given by N=PRtimes PQ.

Concept explainers

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To Calculate: The equation of plane passing through three points (0,2,−1),(1,−3,5)&(3,0,−2)

Want to see the full answer?

Chapter 9 Solutions

The equation of plane passing through three points ( 0 , 2 , − 1 ) , ( 1 , − 3 , 5 ) & ( 3 , 0 , − 2 )