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High School Math Calculus PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

To find volume of parallelepiped having adjacent edges u, v and w

To find volume of parallelepiped having adjacent edges u, v and w

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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Question

Chapter 10.3, Problem 60E

To determine

To find volume of parallelepiped having adjacent edges u, v and w

Expert Solution & Answer

Answer to Problem 60E

Required volume = 16 cubic units

Explanation of Solution

Given information :

Parallelepiped having adjacent edges u, v and w as shown in figure:

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 10.3, Problem 60E

Concept used:

The volume V of a parallelepiped with vector u, v and w as adjacent edges is V=|u.(v×w)|

and

u.(v×w)=|(u1u2u3v1v2v3w1w2w3)|

Where

u=(u1u2u3)v=(v1v2v3)w=(w1w2w3)

Calculation:

From figure u(1,2,−1),v(−1,2,2)and w(2,0,1)

u.(v×w)=|12−1−122201|=2((2×2)−(2×(−1)))+1((1×2)−(2×(−1))) (expanding along row 3)=2(4−(−2))+1(2−(−2))=2×(4+2)+1×(2+2)=(2×6)+(1×4)=12+4=16

The volume V of a parallelepiped

=|u.(v×w)|=|16|=16 cubic units

Conclusion:

The volume V of a parallelepiped with vector u, v and w as adjacent edges is V=16 cubic units

Chapter 10.3, Problem 59E

Chapter 10.3, Problem 61E

Chapter 10 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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

Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.1 - Prob. 41E Ch. 10.1 - Prob. 42E Ch. 10.1 - Prob. 43E Ch. 10.1 - Prob. 44E Ch. 10.1 - Prob. 45E Ch. 10.1 - Prob. 46E Ch. 10.1 - Prob. 47E Ch. 10.1 - Prob. 48E Ch. 10.1 - Prob. 49E Ch. 10.1 - Prob. 50E Ch. 10.1 - Prob. 51E Ch. 10.1 - Prob. 52E Ch. 10.1 - Prob. 53E Ch. 10.1 - Prob. 54E Ch. 10.1 - Prob. 55E Ch. 10.1 - Prob. 56E Ch. 10.1 - Prob. 57E Ch. 10.1 - Prob. 58E Ch. 10.1 - 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