. Resultant of Four Forces An object located at the origin ina three-dimensional coordinate system is held in equilibriumby four forces. One has magnitude 7 lb and points in thedirection of the positive x-axis, so it is represented by thevector 7i. The second has magnitude 24 lb and points inthe direction of the positive y-axis. The third has magnitude25 lb and points in the direction of the negative z-axis.(a) Use the fact that the four forces are in equilibrium (thatis, their sum is 0) to find the fourth force. Express it interms of the unit vectors i, j, and k.(b) What is the magnitude of the fourth force?
. Resultant of Four Forces An object located at the origin ina three-dimensional coordinate system is held in equilibriumby four forces. One has magnitude 7 lb and points in thedirection of the positive x-axis, so it is represented by thevector 7i. The second has magnitude 24 lb and points inthe direction of the positive y-axis. The third has magnitude25 lb and points in the direction of the negative z-axis.(a) Use the fact that the four forces are in equilibrium (thatis, their sum is 0) to find the fourth force. Express it interms of the unit vectors i, j, and k.(b) What is the magnitude of the fourth force?
. Resultant of Four Forces An object located at the origin ina three-dimensional coordinate system is held in equilibriumby four forces. One has magnitude 7 lb and points in thedirection of the positive x-axis, so it is represented by thevector 7i. The second has magnitude 24 lb and points inthe direction of the positive y-axis. The third has magnitude25 lb and points in the direction of the negative z-axis.(a) Use the fact that the four forces are in equilibrium (thatis, their sum is 0) to find the fourth force. Express it interms of the unit vectors i, j, and k.(b) What is the magnitude of the fourth force?
. Resultant of Four Forces An object located at the origin in a three-dimensional coordinate system is held in equilibrium by four forces. One has magnitude 7 lb and points in the direction of the positive x-axis, so it is represented by the vector 7i. The second has magnitude 24 lb and points in the direction of the positive y-axis. The third has magnitude 25 lb and points in the direction of the negative z-axis. (a) Use the fact that the four forces are in equilibrium (that is, their sum is 0) to find the fourth force. Express it in terms of the unit vectors i, j, and k. (b) What is the magnitude of the fourth force?
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
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