Explanation Given: The point is, P 0 ( 0 , 2 , − 2 ) . The parallel plane is, Q : 2 x + y − z = 1 . Definition used: “The plane passing through the point P 0 ( x 0 , y 0 , z 0 ) with a normal vector n = 〈 a , b , c 〉 is described by the equation, a ( x − x 0 ) + b ( y − y 0 ) + c ( z − z 0 ) = 0 ”. Calculation: Let the required plane be R . Thus, the plane R is parallel to the plane Q : 2 x + y − z = 1 . Find a normal vector for Q : 2 x + y − z = 1 to obtain the plane R . The coefficients of x , y and z of the plane Q : 2 x + y − z = 1 are the components of a vector normal to Q : 2 x + y − z = 1 . Thus, the normal vector n of the plane Q : 2 x + y − z = 1 is n = 〈 2 , 1 , − 1 〉

Calculus: Early Transcendentals, 2nd Edition

2nd Edition

ISBN: 9780321965165

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 12.1, Problem 32E

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To find: The equation of the plane which is parallel to the plane Q:2x+y−z=1 and passes through the point, P0(0,2,−2) .

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Chapter 12.1, Problem 31E

Chapter 12.1, Problem 33E

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Calculus: Early Transcendentals, 2nd Edition

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The equation of the plane which is parallel to the plane Q : 2 x + y − z = 1 and passes through the point, P 0 ( 0 , 2 , − 2 ) .

Solution Summary: The author explains the equation of the plane which passes through the point, P_0(0,2,-2).

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To find: The equation of the plane which is parallel to the plane Q:2x+y−z=1 and passes through the point, P0(0,2,−2) .

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Chapter 12 Solutions