Chapter 12.R, Problem 7E

### Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Chapter
Section

### Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

# Suppose that u ⋅ ( v ×  w ) =2 . Find(a) ( u × v ) ⋅ w (b) u ⋅ ( w × v ) (c) v ⋅ ( u × w ) (d) ( u × v ) ⋅ v

To determine

To find:

u×v·w

Explanation

1) Concept:

Use the property of vector cross product

uÃ—vÂ·w=uÂ·vÃ—w

2) Given:

uÂ·vÃ—w=2

3) Calculation:

Since uÃ—vÂ·w=uÂ·vÃ—w, and uÂ·vÃ—w=2 is given

uÃ—vÂ·w=2

Conclusion:

uÃ—vÂ·w=2

To Find:

uÂ·(wÃ—v)

Solution:

-2

1) Concept:

Use the property of vector cross product

uÃ—v=-vÃ—w

2) Given:

uÂ·vÃ—w=2

3) Calculation:

Since uÃ—v=-vÃ—w

uÂ·wÃ—v=uÂ·-vÃ—w

=-uÂ·vÃ—w

And uÂ·vÃ—w=2 is given

uÂ·wÃ—v=-2

Conclusion:

uÂ·wÃ—v=-2

To Find:

vÂ·</

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