Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 6, Problem 12P

(a)

To determine

The angle between the vectors A and B.

(a)

Expert Solution
Check Mark

Answer to Problem 12P

The angle between the vectors A and B is 11.3°_.

Explanation of Solution

Given that A=3.00i^2.00j^ and B=4.00i^4.00j^.

Write the expression for dot product of A and B.

    AB=ABcosθ        (I)

Here, A and B are the vectors, and θ is the angle between A and B.

Rearrange equation (I), to find θ.

    cosθ=AB|A||B|θ=cos1(AB|A||B|)        (II)

Conclusion:

Substitute 3.00i^2.00j^ for A, and 4.00i^4.00j^ for B in equation (II), to find θ.

    θ=cos1((3.00i^2.00j^)(4.00i^4.00j^)(9+4).(16+16))=cos1((12.0+8.00)(9+4).(16+16))=11.3°

Therefore, The angle between the vectors A and B is 11.3°_.

(b)

To determine

The angle between the vectors A and B.

(b)

Expert Solution
Check Mark

Answer to Problem 12P

The angle between the vectors A and B is 156°_.

Explanation of Solution

Given that A=2.00i^+4.00j^ and B=3.00i^4.00j^+2.00k^.

Conclusion:

Substitute 2.00i^+4.00j^ for A, and 3.00i^4.00j^+2.00k^ for B in equation (II), to find θ.

    θ=cos1((2.00i^+4.00j^)(3.00i^4.00j^+2.00k^)(4+16).(9+16+4))=cos1((6.016.00)(20.0).(29.0))=156°

Therefore, The angle between the vectors A and B is 156°_.

(c)

To determine

The angle between the vectors A and B.

(c)

Expert Solution
Check Mark

Answer to Problem 12P

The angle between the vectors A and B is 82.3°_.

Explanation of Solution

Given that A=i^2.00j^+2.00k^ and B=3.00j^+4.00k^.

Conclusion:

Substitute i^2.00j^+2.00k^ for A, and 3.00j^+4.00k^ for B in equation (II), to find θ.

    θ=cos1((i^2.00j^+2.00k^)(3.00j^+4.00k^)(1+4+4).(9+16))=cos1((6.0+8.00)(9).(25.0))=82.3°

Therefore, The angle between the vectors A and B is 82.3°_.

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Chapter 6 Solutions

Principles of Physics: A Calculus-Based Text

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