Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Chapter 10.4, Problem 25E
To determine

To find: The general form of the equation of the plane passing through the point and perpendicular the specified vector.

Expert Solution & Answer
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Answer to Problem 25E

The general form of the equation of the plane passing through the point and perpendicular the specified vector is −2x+y−2z+10=0 .

Explanation of Solution

Given information:

The point is (5,6,3) which perpendicular to n=−2i+j−2k .

Calculation:

The standard equation of the plane is given by a(x−x1)+b(y−y1)+c(z−z1)=0 , where n=〈a,b,c〉 is the nonzero normal vector. So, the normal vector is n=〈−2,1,−2〉 .

Substitute −2 for a , 1 for b , −2 for c , 5 for x1 , 6 for y1 and 3 for z1 in the equation a(x−x1)+b(y−y1)+c(z−z1)=0 to find the general form of the equation of the plane passing through the point and perpendicular the specified vector.

  −2(x−5)+1(y−6)−2(z−3)=0−2x+10+y−6−2z+6=0−2x+y−2z+10=0

Therefore, the general form of the equation of the plane passing through the point and perpendicular the specified vector is −2x+y−2z+10=0 .

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Chapter 10.4, Problem 24E
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Chapter 10.4, Problem 26E

Chapter 10 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 10.1 - Prob. 1ECh. 10.1 - Prob. 2ECh. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10E
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