Chapter 9: Q. 31 (page 627)

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

Short Answer

Expert verified

The required cross product is $- 18 i - 14 j - 6 k$ .

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 $u \times (2 v)$ .

Step 2. Finding cross product

$u = 2 i - 3 j + k v = - 3 i + 3 j + 2 k ∴ 2 v = 2 \times (- 3 i + 3 j + 2 k) \Rightarrow 2 v = - 6 i + 6 j + 4 k$

The required cross product is

$u \times (2 v) = |\begin{matrix} i & j & k \\ 2 & - 3 & 1 \\ - 6 & 6 & 4 \end{matrix}| = i |\begin{matrix} - 3 & 1 \\ 6 & 4 \end{matrix}| - j |\begin{matrix} 2 & 1 \\ - 6 & 4 \end{matrix}| + k |\begin{matrix} 2 & - 3 \\ - 6 & 6 \end{matrix}| = i ((- 3) . 4 - 6.1) - j (2.4 - (- 6) . 1) + k (2.6 - (- 6) . (- 3)) = - 18 i - 14 j - 6 k$

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding 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×2v

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding cross product

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

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