Chapter 9: Q. 34 (page 627)

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

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 $v . (v \times w)$ .

Step 2. Finding cross product

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

The required cross product is

$v \times w = |\begin{matrix} i & j & k \\ - 3 & 3 & 2 \\ 1 & 1 & 3 \end{matrix}| = i |\begin{matrix} 3 & 2 \\ 1 & 3 \end{matrix}| - j |\begin{matrix} - 3 & 2 \\ 1 & 3 \end{matrix}| + k |\begin{matrix} - 3 & 3 \\ 1 & 1 \end{matrix}| = i (3.3 - 1.2) - j ((- 3) . 3 - 1.2) + k ((- 3) . 1 - 1.3) = 7 i + 11 j - 6 k$

Step 3. Finding dot product

The required dot product is

$v . (v \times w) = (- 3 i + 3 j + 2 k) . (7 i + 11 j - 6 k) = (- 3) . 7 + 3.11 + 2 . (- 6) = - 21 + 33 - 12 = 0$

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding cross product

Step 3. Finding dot 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.(v×w)

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding cross product

Step 3. Finding dot product

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Geometry

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Logic and Functions

Study anywhere. Anytime. Across all devices.

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