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High School Math Calculus Precalculus with Limits: A Graphing Approach

The volume of the parallelepiped with the given vertices.

The volume of the parallelepiped with the given vertices.

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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Question

Chapter 10, Problem 51RE

To determine

To find: The volume of the parallelepiped with the given vertices.

Expert Solution & Answer

Answer to Problem 51RE

The volume of parallelepiped with given vertices is 75 cubic units .

Explanation of Solution

Given information:

The given verticesare A(0,0,0) , B(3,0,0) , C(0,5,1) , D(3,5,1) , E(2,0,5) , F(5,0,5) , G(2,5,6) and H(5,5,6) .

Calculation:

Calculate the vector AB→ .

AB→=(3−0,0−0,0−0)=(3,0,0)

Calculate the vector AD→ .

AD→=(3−0,5−0,1−0)=(3,5,1)

Calculate the vector AE→ .

AE→=(2−0,0−0,5−0)=(2,0,5)

Here, AB→ , AD→ and AE→ are the three vector forming the parallelepiped’s length, width and height. To find the volume of parallelepiped, calculate the determinant with these three vectors.

The volume of the parallelepiped is:

(AB→×AD→)⋅AE→=|300351205|=3[5(5)−0(1)]−0[3(5)−2(1)]+0[3(0)−5(2)]=3(25−0)=75

Therefore,the volume of parallelepiped with given vertices is 75 cubic units .

Chapter 10, Problem 50RE

Chapter 10, Problem 52RE

Chapter 10 Solutions

Precalculus with Limits: A Graphing Approach

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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