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# An object located at the origin in a three-dimensional coordinate system is held in equilibrium by 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 27 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 ij, and k.

(b) What is the magnitude of the fourth force? (in lbs)

a ) The fourth force is: . . ( − 7 ﻿ ​ i ​ ^ ​ ​ ﻿ −... View the full answer

a) ﻿ F ​ 4 ​ ​ = − 7 i − 2 4 j + 2 7 k... View the full answer

Part(a) ﻿ ​ F ​ ¯ ​ ​ ​ 4 ​ ​... View the full answer

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