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 33E
To determine

To find: The general form of the equation of the plane passes through (2,5,3) and parallel to the xz -plane.

Expert Solution & Answer
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Answer to Problem 33E

The general form of the equation of the plane passes through (2,5,3) and parallel to the xz -plane is y−5=0 .

Explanation of Solution

Given information:

The plane passes through (2,5,3) and it is parallel to the xz -plane.

Calculation:

To get the normal vector on the xz -plane find the cross product of vectors i and k as shown below.

  n=|ijk100001|=i(0−0)−j(1−0)+k(0−0)=−j=〈0,−1,0〉

Substitute 0 for a , −1 for b , 0 for c , 2 for x1 , 5 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 passes through (2,5,3) and is parallel to the xz -plane.

  0(x−2)−1(y−5)+0(z−3)=0−y+5=0y−5=0

Therefore, the general form of the equation of the plane passes through (2,5,3) and is parallel to the xz -plane is y−5=0 .

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Chapter 10.4, Problem 32E
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Chapter 10.4, Problem 34E

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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