Concept explainers
(a)
Magnitude and direction of vector with components
(a)
Answer to Problem 28P
Vector has magnitude
Explanation of Solution
Write the equation for the magnitude of vector.
Here, the magnitude of vector A is
Write the equation to find the angle made by vector with the x-axis.
Here, the angle made by the vector with the x-axis is
Conclusion:
Substitute
Substitute
It is to be noted that
Here, the angle made by the vector with positive x direction in counterclockwise direction is
Substitute
Therefore, the vector has magnitude
(b)
Magnitude and direction of vector with components
(b)
Answer to Problem 28P
Vector has magnitude
Explanation of Solution
Write the equation for the magnitude of vector.
Here, the magnitude of vector is
Write the equation to find the angle made by vector with the x-axis.
Conclusion:
Substitute
Substitute
It is to be noted that
Here, the angle made by the vector with positive x direction in counterclockwise direction is
Substitute
Therefore, the vector has magnitude
(c)
Magnitude and direction of vector with components
(c)
Answer to Problem 28P
Vector has magnitude
Explanation of Solution
Write the equation for the magnitude of vector.
Here, the magnitude of vector is
Write the equation to find the angle made by vector with the x-axis.
Conclusion:
Substitute
Substitute
It is to be noted that both
Substitute
Therefore, the vector has magnitude
(d)
Magnitude and direction of vector with components
(d)
Answer to Problem 28P
Vector has magnitude
Explanation of Solution
Write the equation for the magnitude of vector.
Here, the magnitude of vector is
Write the equation to find the angle made by vector with the x-axis.
Conclusion:
Substitute
Substitute
It is to be noted that both
Therefore, the vector has magnitude
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