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High School Math Calculus Precalculus with Limits: A Graphing Approach

ToEvaluate: The triple scalar product of the vectors u = i + 4 j − 7 k , v = 2 i + 4 k and w = − 3 j + 6 k

ToEvaluate: The triple scalar product of the vectors u = i + 4 j − 7 k , v = 2 i + 4 k and w = − 3 j + 6 k

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 10.3, Problem 56E

To determine

ToEvaluate:The triple scalar product of the vectors u=i+4j−7k , v=2i+4k and w=−3j+6k

Expert Solution & Answer

Answer to Problem 56E

The triple scalar product u·(v×w)=3

Explanation of Solution

Given:

The vectors u=i+4j−7k , v=2i+4k and w=−3j+6k

Concept Used:

For the three vectors u=〈u1,u2,u3〉 , v=〈v1,v2,v3〉 and w=〈w1,w2,w3〉 ,the triple scalar product of them can be calculated as

u·(v×w)=|u1u2u3v1v2v3w1w2w3|

Calculation:

Forthe vectors u=i+4j−7k , v=2i+4k and w=−3j+6k

u·(v×w)=|14−72040−36|=1|04−36|−2|4−7−36|+0|4−704|=1((0)(6)−(−3)(4))−3((4)(6)−(−3)(−7))+0((4)(4)−(0)(−7))=1(0+12)−3(24−21)+0(16+0)

=1(12)−3(3)+0(16)=12−9+0=3

Therefore, u·(v×w)=3

Conclusion:

The triple scalar product u·(v×w)=3

Chapter 10.3, Problem 55E

Chapter 10.3, Problem 57E

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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