Chapter 10: Q. 17 (page 824)

If u, v and w are three vectors in $ℝ^{3}$ , what is wrong with the expression $u \times v \times w$ ?

Short Answer

Expert verified

The cross product is not associative, so we must specify whether we mean $(u \times v) \times w or u \times (v \times w)$ .

Step by step solution

Step 1. Given Information

If u, v and w are three vectors in $ℝ^{3}$ , we have to explain what is wrong with the expression $u \times v \times w$ .

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

$u \cdot (v \times w) = v \cdot (w \times u) = w \cdot (u \times v)$

But the given expression is $u \times v \times w$ which is wrong expression because the cross product is not associative, so we must specify whether we mean $(u \times v) \times w or u \times (v \times w)$

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If u, v and w are three vectors in $ℝ^{3}$ , what is wrong with the expression $u \times v \times w$ ?

Short Answer

Step by step solution

Step 1. Given Information

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

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If u, v and w are three vectors in ℝ3, what is wrong with the expression u×v×w?

Short Answer

Step by step solution

Step 1. Given Information

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

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If u, v and w are three vectors in $ℝ^{3}$ , what is wrong with the expression $u \times v \times w$ ?