   Chapter 12.R, Problem 7E

Chapter
Section
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

u×v·w=u·v×w

2) Given:

u·v×w=2

3) Calculation:

Since u×v·w=u·v×w, and u·v×w=2 is given

u×v·w=2

Conclusion:

u×v·w=2

To Find:

u·(w×v)

Solution:

-2

1) Concept:

Use the property of vector cross product

u×v=-v×w

2) Given:

u·v×w=2

3) Calculation:

Since u×v=-v×w

u·w×v=u·-v×w

=-u·v×w

And u·v×w=2 is given

u·w×v=-2

Conclusion:

u·w×v=-2

To Find:

v·</

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