Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 11, Problem 11.1QQ

Which of the following statements about the relationship between the magnitude of the cross product of two vectors and the product of the magnitudes of the vectors is true? (a) | A × B | is larger than AB. (b) | A × B | is smaller than AB. (c) | A × B | could be larger or smaller than AB, depending on the angle between the vectors. (d) | A × B | could he equal to AB.

Expert Solution & Answer
Check Mark
To determine

The statement that is true about the relationship between the magnitude of the cross product of two vectors and the product of the magnitude of the vector.

Answer to Problem 11.1QQ

Option(d).

Explanation of Solution

The magnitude of the cross product of two vector that is A and B is,

    |A×B|=ABsinθ

Here, θ is the angle between the two vectors.

The value of |A×B| is a function of sinθ so the value depends on the angle between the two vectors. As the angle varies between the two vectors, the magnitude of the cross product of the two vectors also changed. When, θ is π2, sinθ is 1 and hence |A×B| equals AB.

Conclusion:

When both A and B are perpendicular,  |A×B| equals AB Thus, option (d) is correct.

The value of sinθ is never greater than 1 and hence |A×B| is lesser than AB. Thus, option (a) is incorrect.

|A×B| is smaller than AB for every other angle except π2. Thus, option (b) is incorrect.

From option (b) and (c), |A×B| is couldn’t be always larger or smaller with regard to the angle. Thus, option (c) is incorrect.

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Chapter 11 Solutions

Physics for Scientists and Engineers, Technology Update (No access codes included)

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