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.