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 10.4, Problem 60E
To determine

To find: the angle between two adjacent sides of the pan.

Expert Solution & Answer
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Answer to Problem 60E

The angle between two adjacent sides of the pan is 86.34∘ .

Explanation of Solution

Given information:

The figure provided in the question,

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 10.4, Problem 60E

Calculation: from the above graph it can be observed that, the one side of the pan is the plane passing through the points (0,0,0),(−1,−1,7) and (9,19,7) .

The component form of vectors for plane,

  u=〈−1−0,−1−0,7−0〉u=〈−1,−1,7〉                   [subtract]v=〈9−0,19−0,7−0〉v=〈9,19,7〉                      [subtract]

The normal vector to the plane,

  u×vijk=−1−179197u×v=i(−7−133)−j(−7−63)+k(−19+9)     [simplify]u×v=−140i+70j−10k

The general equation of the plane can be written as,

  a(x−x1)+b(y−y1)+c(z−z1)=0−140(x−0)+70(y−0)+(−10)(z−0)=0    [substitute]−140x+70y−10z=0                                         [multiply]14x−7y+z=0                                                       [simplify]

Thus, the general equation of the plane of the first side of the pan is 14x−7y+z=0 .

The one side of the pan is the plane passing through the point (0,0,0),(8,0,0) and (8,18,0)

The component form of vectors for plane,

  u=〈8−0,0−0,0−0〉u=〈8,0,0〉                   [subtract]v=〈8−0,18−0,0−0〉v=〈8,18,0〉                      [subtract]

The normal vector to the plane,

  u×v=ijk8008180u×v=i(0−0)−j(0−0)+k(144−0)     [simplify]u×v=144k

The general equation of the plane can be written as,

  a(x−x1)+b(y−y1)+c(z−z1)=00(x−0)+0(y−0)+144(z−0)=0    [substitute]144z=0                                         [multiply]z=0                                                       [simplify]

Thus, the another plane general equation is z=0 .

The angle between both is ,

  cosθ=〈14,−7,1〉·〈0,0,1〉|〈1,−1,0〉||〈0,0,1〉|cosθ=1246     [dot product]cosθ=246246θ=86.34∘

Thus, The angle between two adjacent sides of the pan is 86.34∘ .

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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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