A force 25 N makes an angle of 30,45 and 75 degree with x, y and z axis. What should be the corresponding force vector?

F = (21.651N, 17.678N, 6.470N)

Explanation:

The components of a vector in R ^ 3 are given according to their cosine directors, therefore, if we name F the force of 25N and Fx, Fy and Fz the components of the force with respect to the X, Y and Z axes, respectively:

Fx = FCos30 = 25 (0.866) = 21.651

Fy = FCos45 = 25 (0.707) = 17.678

Fz = FCos75 = 25 (0.259) = 6.470

F = (21.651N, 17.678N, 6.470N)