Chapter 10: Q. 30 (page 824)

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

Short Answer

Expert verified

The value of $u \times v = 5 i - 7 j - 2 k and v \times u = - 5 i + 7 j + 2 k$ .

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 $u \times v and v \times u$ .

Step 2. Firstly finding the value of u×v

The value of vectors $u = (- 3, 1, - 4), v = (2, 0, 5)$

The cross product of $u \times v$

$u \times v = \det [\begin{matrix} i & j & k \\ - 3 & 1 & - 4 \\ 2 & 0 & 5 \end{matrix}]$

Step 3. Now solving the matrix.

$u \times v = \det [\begin{matrix} i & j & k \\ - 3 & 1 & - 4 \\ 2 & 0 & 5 \end{matrix}] u \times v = ((1) (5) - (- 4) (0)) i + ((- 3) (5) - (- 4) (2)) j + ((- 3) (0) - (1) (2)) k u \times v = (5 - 0) i + (- 15 + 8) j + (0 - 2) k u \times v = 5 i - 7 j - 2 k$

Step 4. Now finding the value of v×u

The value of vectors $u = (- 3, 1, - 4), v = (2, 0, 5)$

The cross product of

localid="1649439993393" $v \times u = \det [\begin{matrix} i & j & k \\ 2 & 0 & 5 \\ - 3 & 1 & - 4 \end{matrix}]$

Step 5. Now solving the matrix.

$v \times u = \det [\begin{matrix} i & j & k \\ 2 & 0 & 5 \\ - 3 & 1 & - 4 \end{matrix}] v \times u = ((0) (- 4) - (5) (1)) i + ((2) (- 4) - (- 3) (5)) j + ((2) (1) - (- 3) (0)) k v \times u = (0 - 5) i + (- 8 + 15) j + (2 - 0) k v \times u = - 5 i + 7 j + 2 k$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Firstly finding the value of u×v

Step 3. Now solving the matrix.

Step 4. Now finding the value of v×u

Step 5. Now solving the matrix.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Logic and Functions

Discrete Mathematics

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Firstly finding the value of u×v

Step 3. Now solving the matrix.

Step 4. Now finding the value of v×u

Step 5. Now solving the matrix.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Logic and Functions

Discrete Mathematics

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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