   Chapter 11.4, Problem 41E

Chapter
Section
Textbook Problem

# EXPLORING CONCEPTSComparing Dot Products Identify the dot products that are equal. Explain your reasoning. (Assume u, v, and w are nonzero vectors.)(a) u ⋅ ( v × w ) (c) ( u × v ) ⋅ w (e) u ⋅ ( w × v ) (g) ( − u × v ) ⋅ w (b) ( v × w ) ⋅ u (d) ( u × − w ) ⋅ v (f) w ⋅ ( v × u ) (h) ( w × u ) ⋅ v

To determine

To calculate: Which of the provided dot products are equal.

Explanation

Given:

(a)u·(v×w)

(b) (v×w)·u

(c) (u×v)·w

(d) (u×w)·v

(e) u·(w×v)

(f) w·(v×u)

(g) (u×v)·w

(h) (w×u)·v

Formula used:

Calculation: It is known that,

u·(v×w)=|u1u2u3v1v2v3w1w2w3|

a)u.(v×w)=(v×w)

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