Compute the magnitude and direction of the force:

Problem:

Compute the magnitude and direction of the force

F¯ = (320 N) i¯ + (450 N) j¯ - (600 N) k¯

Solution

The magnitude of the force F is specified by

          = 815.41N

cos θ_x = F_x / F =            320 /815.41 = 0.3924

∴ θ _x = 66^o  53′ 36′

cos θ _y = F_y/  F

 = 450 / 815.41

 = 0.5519

∴ θ _y = 56^o  30′ 16′

cos θ_z = F_z /F =  - 600 / 815.41 = - 0.7358

∴ θ_z = 137^o  22′ 29′′

Therefore, the force of 815.41 N is making an angle of 66^o 53′ 36′′ along with x axis, 56^o 30′ 16′′ along y axis and 137^o 22′ with z axis.