Chapter 9: Q. 39 (page 627)

Use the given vectors u, v, and w to find each expression.
$u = 2 i - 3 j + k, v = - 3 i + 3 j + 2 k, w = i + j + 3 k u \times (v \times v)$

Short Answer

Expert verified

The required value of the expression is $0$ .

Step by step solution

Step 1. Given Information

We are given three vectors $(u, v, w)$ and we need to find the cross product of $u \times (v \times v)$ .

Step 2. Finding first cross product

$u = 2 i - 3 j + k v = - 3 i + 3 j + 2 k$

The required cross product is

$v \times v = |\begin{matrix} i & j & k \\ - 3 & 3 & 2 \\ - 3 & 3 & 2 \end{matrix}| = i |\begin{matrix} 3 & 2 \\ 3 & 2 \end{matrix}| - j |\begin{matrix} - 3 & 2 \\ - 3 & 2 \end{matrix}| + k |\begin{matrix} - 3 & 3 \\ - 3 & 3 \end{matrix}| = i (3.2 - 3.2) - j ((- 3) . 2 - (- 3) . 2) + k ((- 3) . 3 - (- 3) . 3) = 0$

$∴ u \times (v \times v) = u \times 0 = 0$

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Use the given vectors u, v, and w to find each expression.
$u = 2 i - 3 j + k, v = - 3 i + 3 j + 2 k, w = i + j + 3 k u \times (v \times v)$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding first cross product

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Use the given vectors u, v, and w to find each expression. u=2i-3j+k,v=-3i+3j+2k,w=i+j+3ku×(v×v)

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding first cross product

One App. One Place for Learning.

Most popular questions from this chapter

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Calculus

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Use the given vectors u, v, and w to find each expression.
$u = 2 i - 3 j + k, v = - 3 i + 3 j + 2 k, w = i + j + 3 k u \times (v \times v)$