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Chapter 10, Problem 24P

(a)

To determine

Evaluate cos1[AB/AB].

(a)

Expert Solution
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Answer to Problem 24P

It is found that cos1[AB/AB]=168°_.

Explanation of Solution

The vector A is given by.

  A=3i^+7j^4k^

Vector B is given as.

  B=6i^10j^+9k^

Take the dot product of vector A, and B.

  AB=(3i^+7j^4k^)(6i^10j^+9k^)=3.00(6.00)+7.00(10.0)+(4.00)(9.00)=124

Calculate the magnitude of vector AB.

  AB=(3.00)2+(7.00)2+(4.00)2(6.00)2+(10.0)2+(9.00)2=127

Conclusion:

Substitute, 124 for AB, and 127 for AB in cos1[AB/AB].

  cos1[AB/AB]=cos1(124127)=cos1(0.979)=168°

Therefore, cos1[AB/AB] is equal to 168°_.

(b)

To determine

Evaluate sin1[|A×B|/AB].

(b)

Expert Solution
Check Mark

Answer to Problem 24P

It is found that sin1[|A×B|/AB]=11.9°_.

Explanation of Solution

Take the cross product of vector A, and B.

  A×B=|i^j^k^3.007.004.006.0010.09.00|=23.0i^+3.00j^12.0k^

Consider the magnitude of A×B.

  |A×B|=(23.0)2+(3.00)2+(12.0)2=26.1

Conclusion:

Substitute, 26.1 for |A×B|, 127 for AB in sin1[|A×B|/AB].

  sin1[|A×B|/AB]=sin1(26.1127)=11.9°

Therefore, the sin1[|A×B|/AB]=11.9°_.

(c)

To determine

Out of the above two methods which gives the angle between vectors.

(c)

Expert Solution
Check Mark

Answer to Problem 24P

The first method gives the angle between vectors.

Explanation of Solution

It sis known that sin(180θ) is equal to sinθ, but cos(180θ) is equal to cosθ. The first one sin(180θ) makes no difference between 180θ and θ.

Hence the method in part (a) gives the angle between vectors.

Conclusion:

Therefore, the first method gives the angle between vectors.

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Chapter 10 Solutions

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