   Chapter 12.4, Problem 23E

Chapter
Section
Textbook Problem

# Prove the property of cross products (Theorem 11).23. Properly 1: a × b = −b × a

To determine

To prove: The Property 1 that is (a×b)=b×a .

Explanation

Consider a=a1,a2,a3 and b=b1,b2,b3 .

Find the cross product between a and b .

a×b=|ijka1a2a3b1b2b3|=|a2a3b2b3|i|a1a3b1b3|j+|a1a2b1b2|k=(a2b3a3b2)i(a1b3a3b1)j+(a1b2a2b1)k=(a2b3a3b2),(a3b1a1b3),(a1b2a2b1)

a×b=(1)(b2a3b3a2),(1)(b3a1b1a3),(1)(b1a2b2a1)=1(b2a3b3a2),(b3a1b1a3),(b1a2b2a1)

a×b=(b2a3b3a2),(b3a1b1a3),(b1a2b2a1) (1)

Find b×a

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find the median for the following set of scores: 1, 9, 3, 6, 4, 3, 11, 10

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### In Exercises 1-6, simplify the expression. 2. 2a23ab9b22ab2+3b3

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### True or False: is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th 