Concept explainers
The rectangle shown in Figure P3.56 has sides parallel to the x and y axes. The position vectors of two corners are = 10.0 m at 50.0° and = 12.0 m at 30.0°. (a) Find the perimeter of the rectangle. (b) Find the magnitude and direction of the vector from the origin to the upper-right corner of the rectangle.
(a)
The perimeter of the rectangle.
Answer to Problem 3.56AP
The perimeter of the rectangle is
Explanation of Solution
Given info: The rectangle has sides parallel to the
The vector component of
Here,
Substitute
Thus, the vector component of
The vector component of
Here,
Substitute
Thus, the vector component of
The position vector
Here,
Substitute
Thus, the position vector for the vector
The component of vector
Here,
Substitute
Thus, the component of vector
The component of vector
Here,
Substitute
Thus, the component of vector
The position vector of the vector
Here,
Substitute
Thus, the position vector of the vector
The length of the rectangle is,
Here,
The width of the rectangle is,
Here,
The vector
Substitute
Formula to calculate the perimeter of the rectangle is,
Here,
Substitute
Conclusion:
Therefore, the perimeter of the rectangle is
(b)
The magnitude and direction of the vector from the origin to the upper right coordinate of the rectangle.
Answer to Problem 3.56AP
The magnitude and direction of the vector from the origin to the upper right coordinate of the rectangle is
Explanation of Solution
Given info: The rectangle has sides parallel to the
The vector of point
The vector
Here,
Substitute
Formula to calculate the magnitude of vector
Here,
Substitute
Formula to calculate the angle made by the vector
Here,
Substitute
Conclusion:
Therefore, the magnitude and direction of the vector from the origin to the upper right coordinate of the rectangle is
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