Chapter 9: Q. 30 (page 627)

Use the given vectors u, v, and w to find each expression.
$u = 2 i - 3 j + k, v = - 3 i + 3 j + 2 k, w = i + j + 3 k v \times (4 w)$

Short Answer

Expert verified

The required cross product is $28 i + 44 j - 24 k$ .

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 $v \times (4 w)$ .

Step 2. Finding cross product

$v = - 3 i + 3 j + 2 k w = i + j + 3 k ∴ (4 w) = 4 \times (i + j + 3 k) \Rightarrow 4 w = 4 i + 4 j + 12 k$

The required cross product is

$v \times (4 w) = |\begin{matrix} i & j & k \\ - 3 & 3 & 2 \\ 4 & 4 & 12 \end{matrix}| = i |\begin{matrix} 3 & 2 \\ 4 & 12 \end{matrix}| - j |\begin{matrix} - 3 & 2 \\ 4 & 12 \end{matrix}| + k |\begin{matrix} - 3 & 3 \\ 4 & 4 \end{matrix}| = i (3.12 - 4.2) - j ((- 3) . 12 - 4.2) + k ((- 3) . 4 - 3.4) = 28 i + 44 j - 24 k$

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Use the given vectors u, v, and w to find each expression.
$u = 2 i - 3 j + k, v = - 3 i + 3 j + 2 k, w = i + j + 3 k v \times (4 w)$

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+3kv×4w

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

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Decision Maths

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Study anywhere. Anytime. Across all devices.

Use the given vectors u, v, and w to find each expression.
$u = 2 i - 3 j + k, v = - 3 i + 3 j + 2 k, w = i + j + 3 k v \times (4 w)$