Explanation If the two planes are parallel, the normal vectors of both the planes are scalar multiples of each other. Write the equation of plane P 1 . 3 x + 6 y − 3 z = 6 Write the normal vector from the plane P 1 as follows. n 1 = 〈 3 , 6 , − 3 〉 Write the equation of plane P 2 . 4 x − 12 y + 8 z = 5 Write the normal vector from the plane P 2 as follows. n 2 = 〈 4 , − 12 , 8 〉 Write the equation of plane P 3 . 9 y = 1 + 3 x + 6 z Rewrite the equation as follows. 3 x − 9 y + 6 z = − 1 Write the normal vector from the plane P 3 as follows. n 3 = 〈 3 , − 9 , 6 〉 Write the equation of plane P 4 . z = x + 2 y − 2 Rewrite the equation as follows. x + 2 y − z = 2 Write the normal vector from the plane P 4 as follows. n 4 = 〈 1 , 2 , − 1 〉 The normal vector n 1 is also written as follows. n 1 = 〈 3 , 6 , − 3 〉 = ( 3 ) 〈 1 , 2 , − 1 〉 = ( 3 ) n 4 The normal vectors n 1 and n 4 are scalar multiples of each other

8th Edition

ISBN: 9781305266643

Author: James Stewart

Publisher: Cengage Learning

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Chapter 12.5, Problem 67E

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To identify: The parallel planes among the four planes P1:3x+6y−3z=6, P2:4x−12y+8z=5, P3:9y=1+3x+6z, and P4:z=x+2y−2.

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Chapter 12.5, Problem 66E

Chapter 12.5, Problem 68E

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The parallel planes among the four planes P 1 : 3 x + 6 y − 3 z = 6 , P 2 : 4 x − 12 y + 8 z = 5 , P 3 : 9 y = 1 + 3 x + 6 z , and P 4 : z = x + 2 y − 2 .

Solution Summary: The author explains that the parallel planes are parallel to each other, and the normal vectors of both are scalar multiples.

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To identify: The parallel planes among the four planes P1:3x+6y−3z=6, P2:4x−12y+8z=5, P3:9y=1+3x+6z, and P4:z=x+2y−2.

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Chapter 12 Solutions