Explanation Given information: Plane passing through A ( 0 , 0 , 0 ) ,B ( 1 , 4 , − 1 ) &C ( 2 , − 1 , 3 ) and a point P ( − 4 , 3 , 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. Distance of a point from the plane is d = | A x 0 + B y 0 + Cz 0 +D | A 2 + B 2 + C 2 Calculation: The plane is passing through the points A ( 0 , 0 , 0 ) ,B ( 1 , 4 , − 1 ) &C ( 2 , − 1 , 3 ) , therefore the normal to the plane is given by N = A B × A C A B =PV of B − PV of A A ( 0 , 0 , 0 ) ,B ( 1 , 4 , − 1 ) &C ( 2 , − 1 , 3 ) A B = ( 1 − 0 ) i + ( 4 − 0 ) j + ( − 1 − 0 ) k = 1 i + 4 j − 1 k A C = PV of C − PV of A A ( 0 , 0 , 0 ) ,B ( 1 , 4 , − 1 ) &C ( 2 , − 1 , 3 ) A C = ( 2 − 0 ) i + ( − 1 − 0 ) j + ( 3 − 0 ) k = 2 i − 1 j + 3 k N = A B × A C N =

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

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

Publisher: Kendall Hunt Publishing

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Chapter 9, Problem 36SP

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To Calculate: The distance of a plane passing through A(0,0,0),B(1,4,−1)&C(2,−1,3) from the point P(−4,3,2)

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Chapter 9, Problem 35SP

Chapter 9, Problem 37SP

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Chapter 9 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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The distance of a plane passing through A ( 0 , 0 , 0 ) ,B ( 1 , 4 , − 1 ) &C ( 2 , − 1 , 3 ) from the point P ( − 4 , 3 , 2 )

Solution Summary: The author calculates the distance of a plane passing through Aleft, B left, and P(-4,3,2). The normal to the plane is given by N=PRtimes PQ.

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To Calculate: The distance of a plane passing through A(0,0,0),B(1,4,−1)&C(2,−1,3) from the point P(−4,3,2)

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Chapter 9 Solutions

The distance of a plane passing through A ( 0 , 0 , 0 ) ,B ( 1 , 4 , − 1 ) &amp;C ( 2 , − 1 , 3 ) from the point P ( − 4 , 3 , 2 )

Solution Summary: The author calculates the distance of a plane passing through Aleft, B left, and P(-4,3,2). The normal to the plane is given by N=PRtimes PQ.

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To Calculate: The distance of a plane passing through A(0,0,0),B(1,4,−1)&C(2,−1,3) from the point P(−4,3,2)

Want to see the full answer?

Chapter 9 Solutions

The distance of a plane passing through A ( 0 , 0 , 0 ) ,B ( 1 , 4 , − 1 ) &C ( 2 , − 1 , 3 ) from the point P ( − 4 , 3 , 2 )