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High School Math Calculus Precalculus with Limits: A Graphing Approach

Whether the statement “The cross product is not defined for vectors in the plane.” is true or false.

Whether the statement “The cross product is not defined for vectors in the plane.” is true or false.

Precalculus with Limits: A Graphing Approach

Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

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Question

Chapter 10.3, Problem 65E

To determine

Whether the statement “The cross product is not defined for vectors in the plane.” is true or false.

Expert Solution & Answer

Answer to Problem 65E

The statement “The cross product is not defined for vectors in the plane.” is true.

Explanation of Solution

Given information:

The statement “The cross product is not defined for vectors in the plane.”

Consider the provided statement “The cross product is not defined for vectors in the plane.”

According to the definition of cross product if there are two three-dimensional vectors in a space given in the form of their components, say, a=〈a1,a2,a3〉 and b=〈b1,b2,b3〉 , then the cross product of two vectors is defined as ,

a×b=ijka1a2a3b1b2b3= (a2b3−a3b2 )i−(a1b3−a3b1)j+(a1b2−a2b1)k

Therefore, the cross product is not defined for vectors in two dimensional space.

Thus, the statement “The cross product is not defined for vectors in the plane.” is true.

Chapter 10.3, Problem 64E

Chapter 10.3, Problem 66E

Chapter 10 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

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