Chapter 10: Q. 31 (page 824)

In Exercises 30–35 compute the indicated quantities when $u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$
$u \times w and w \times u$

Short Answer

Expert verified

The value of $u \times w = 25 i - 35 j - 10 k and w \times u = - 25 i + 35 j + 10 k$

Step by step solution

Step 1. Given Information

The indicated quantities when $u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$

We have to find the value of $u \times w and w \times u$

Step 2. Firstly finding the value of u×w

The value of vectors $u = (- 3, 1, - 4) and w = (1, 3, 13)$

The cross product of

$u \times w = \det [\begin{matrix} i & j & k \\ - 3 & 1 & - 4 \\ 1 & 3 & 13 \end{matrix}]$

Step 3. Now solving the matrix.

$u \times w = \det [\begin{matrix} i & j & k \\ - 3 & 1 & - 4 \\ 1 & 3 & 13 \end{matrix}] u \times w = ((1) (13) - (- 4) (3)) i + ((- 3) (13) - (- 4) (1)) j + ((- 3) (3) - (1) (1)) k u \times w = (13 + 12) i + (- 39 + 4) j + (- 9 - 1) k u \times w = 25 i - 35 j - 10 k$

Step 4. Now finding the value of w×u

The value of vectors $u = (- 3, 1, - 4) and w = (1, 3, 13)$

The cross product of

$w \times u = \det [\begin{matrix} i & j & k \\ 1 & 3 & 13 \\ - 3 & 1 & - 4 \end{matrix}]$

Step 5. Now solving the matrix.

$w \times u = \det [\begin{matrix} i & j & k \\ 1 & 3 & 13 \\ - 3 & 1 & - 4 \end{matrix}] w \times u = ((- 4) (3) - (1) (13)) i + ((- 4) (1) - (- 3) (13)) j + ((1) (1) - (- 3) (3)) k w \times u = (- 12 - 13) i + (- 4 + 39) j + (1 + 9) k w \times u = - 25 i + 35 j + 10 k$

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In Exercises 30–35 compute the indicated quantities when $u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$
$u \times w and w \times u$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Firstly finding the value of u×w

Step 3. Now solving the matrix.

Step 4. Now finding the value of w×u

Step 5. Now solving the matrix.

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In Exercises 30–35 compute the indicated quantities when u=(−3,1,−4),v=(2,0,5),andw=(1,3,13)u×wandw×u

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Firstly finding the value of u×w

Step 3. Now solving the matrix.

Step 4. Now finding the value of w×u

Step 5. Now solving the matrix.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Exercises 30–35 compute the indicated quantities when $u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$
$u \times w and w \times u$