PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Chapter 10, Problem 15CT
To determine

Tofind:the general form of the equation of the plane.

Expert Solution & Answer
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Answer to Problem 15CT

The general form of the equation of the plane is 5x−4y−32z−65=0 .

Explanation of Solution

Given information:

Passing points are (−3,−4,2),(−3,4,1),(1,1,−2)

Calculation:to find the equation of the plane, first find the vector that is normal to the plane.

So find the normal vector,

  u=〈−3+3,4+4,1−2〉u=〈0,8,−1〉               [subtract]v=〈1+3,1+4,−2−2〉v=〈4,5,0〉                             [subtract]

So the normal vector to the plane is,

  n=u×vn=ijk08−1450n=(0+5)i−j(0+4)+k(0−32)   [simplify]n=5i−4j−32k

Since perpendicular vector is n=5i−4j−32k , so direction numbers for n are a=5,b=−4,c=−32 .

And the point is (1,1,−2) ,

So the general equation can be defined as:

  a(x−x1)+b(y−y1)+c(z−z1)=05(x−1)−4(y−1)+(−32)(z+2)=0      [substitute]5x−5−4y+4−32z−64=0                       [multiply]5x−4y−32z−65=0                             [simplify]

Thus, the general equation is 5x−4y−32z−65=0 .

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Chapter 10, Problem 14CT
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Chapter 10, Problem 16CT

Chapter 10 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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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Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - Prob. 26ECh. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - Prob. 31ECh. 10.4 - Prob. 32ECh. 10.4 - Prob. 33ECh. 10.4 - Prob. 34ECh. 10.4 - Prob. 35ECh. 10.4 - Prob. 36ECh. 10.4 - Prob. 37ECh. 10.4 - Prob. 38ECh. 10.4 - Prob. 39ECh. 10.4 - Prob. 40ECh. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.4 - Prob. 43ECh. 10.4 - Prob. 44ECh. 10.4 - Prob. 45ECh. 10.4 - Prob. 46ECh. 10.4 - Prob. 47ECh. 10.4 - Prob. 48ECh. 10.4 - Prob. 49ECh. 10.4 - Prob. 50ECh. 10.4 - Prob. 51ECh. 10.4 - Prob. 52ECh. 10.4 - Prob. 53ECh. 10.4 - Prob. 54ECh. 10.4 - Prob. 55ECh. 10.4 - Prob. 56ECh. 10.4 - Prob. 57ECh. 10.4 - Prob. 58ECh. 10.4 - Prob. 59ECh. 10.4 - Prob. 60ECh. 10.4 - Prob. 61ECh. 10.4 - Prob. 62ECh. 10.4 - Prob. 63ECh. 10.4 - 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