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Chapter 10: Q. 17 (page 824)

If u, v and w are three vectors in 鈩�3, what is wrong with the expression u脳v脳w?

Short Answer

Expert verified

The cross product is not associative, so we must specify whether we mean (u脳v)脳woru脳(v脳w).

Step by step solution

01

Step 1. Given Information

If u, v and w are three vectors in 鈩�3, we have to explain what is wrong with the expression u脳v脳w.

02

Step 2. Let u, v and w be vectors in ℝ3. Then the expression is

u路(v脳w)=v路(w脳u)=w路(u脳v)

But the given expression is u脳v脳wwhich is wrong expression because the cross product is not associative, so we must specify whether we mean(u脳v)脳woru脳(v脳w)

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