(a)
The value of
(a)
Answer to Problem 6P
The value of given expression
Explanation of Solution
Write the expression for the magnitude of
Here,
Write the expression for the magnitude of
Here,
Write the expression for dot product of a vector
Consider the angle for a given expression is
Write the expression for the angle between the vectors.
Substitute
Conclusion:
Substitute
Thus, the value of the given expression
(b)
The value of
(b)
Answer to Problem 6P
The value of the given expression
Explanation of Solution
Write the expression for cross product of two vectors
Simplify the above-obtained expression as.
Write the expression for the magnitude of
Here,
Write the expression for the angle between the vectors.
Substitute
Conclusion:
Substitute
Substitute
Thus, the value of the given expression
(c)
The correct method which gives the angle between two vectors.
(c)
Answer to Problem 6P
The first method gives the angle between the two vectors more accurately.
Explanation of Solution
Write the expression for the angle between the two vectors
Conclusion:
The RHS expression of the equation (VIII) is similar to expression asked in first part.
The angle calculation between two vectors will be correct when using the first method.
Generally, the angle between the two vectors can only be at most
Thus, the first method gives the angle between the two vectors more accurately.
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Chapter 11 Solutions
Physics: for Science.. With Modern. -Update (Looseleaf)
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