Concept explainers
(a)
The magnitude and direction of the vector.
(a)
Answer to Problem 56P
The magnitude and direction of the vector is
Explanation of Solution
Write the expression to determine the magnitude of the vector.
Write the expression to determine the direction of the vector.
Calculate the components of each given vectors by substituting
Solve for
The magnitude of the vector from expression (I)
The direction of the vector from expression (II)
Conclusion:
The magnitude and direction of the vector is
(b)
The magnitude and direction of the vector.
(b)
Answer to Problem 56P
The magnitude and direction of the vector is
Explanation of Solution
Write the expression to determine the magnitude of the vector.
Write the expression to determine the direction of the vector.
Calculate the components of each given vectors by substituting
Solve for
The magnitude of the vector from expression (I)
The direction of the vector from expression (II)
Conclusion:
The magnitude and direction of the vector is
(c)
The magnitude and direction of the vector.
(c)
Answer to Problem 56P
The magnitude and direction of the vector is
Explanation of Solution
Write the expression to determine the magnitude of the vector.
Write the expression to determine the direction of the vector.
Calculate the components of each given vectors by substituting
Solve for
The magnitude of the vector from expression (I)
The direction of the vector from expression (II)
Conclusion:
The magnitude and direction of the vector is
(d)
The magnitude and direction of the vector.
(d)
Answer to Problem 56P
The magnitude and direction of the vector is
Explanation of Solution
Write the expression to determine the magnitude of the vector.
Write the expression to determine the direction of the vector.
Calculate the components of each given vectors by substituting
Solve for
The magnitude of the vector from expression (I)
The direction of the vector from expression (II)
Conclusion:
The magnitude and direction of the vector is
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Chapter 1 Solutions
College Physics, Volume 1
- At one point in space, the direction of the electric field vector Is given In the Cartesian system by the unit vector . If the magnitude of the electric field vector is E=400.0V/m , what are the scalar components , and of the electric field vector at this point? What is the direction angle of the electric field vector at this point?arrow_forwardTwo points in the xy plane have Cartesian coordinates (2.00, 4.00) m and (3.00, 3.00) m. Determine (a) the distance between these points and (b) their polar coordinates.arrow_forwardFigure 1.19 shows two vectors lying in the xy-plane. Determine the signs of the x- and y-components of A, B, and A+B.arrow_forward
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- Vector B has x, y, and z components of 4.00, 6.00, and 3.00 units, respectively. Calculate (a) the magnitude of B and (b) the angle that B makes with each coordinate axis.arrow_forwardRectangular coordinates of a point are given by (2,y) and its polar coordinates are given by (r,/6) . Find y y and r .arrow_forwardFor the two vectors find A − B and |A – B| component of B along A angle between A and B A × B (A − B) × (A + B)arrow_forward
- Show that the force vector is orthogonal to the force vectorarrow_forwardFor what values of a are the vectors A = 2ai − 2j + ak and B = ai + 2aj + 2k perpendicular?arrow_forwardA pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m), (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P1.69. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure 1.69arrow_forward
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