Express the force in vector form:

A force of 400 N forms angles of 45^o, 65^o and 120^o, respectively, along with the x, y and z axes. Express the force in vector form.

Solution

Substituting     F = 400 N, θ_x = 45^o, θ_y = 60^o and θ_z = 120^o, we obtain

F_x  = F cos θ_x = 400 cos 45^o  = 282.84 N

F_y  = F cos θ _y  = 400 cos 60^o  = 200.00 N

F_z  = F cos θ_z  = 400 cos 120^o  = - 200.00 N

F¯ = F¯_x i¯ + F¯_y  j¯ + F¯_z k¯

= (282.84 N) i¯ + (200.00 N) j¯ + (- 200.00 N) k¯

= 282.84i¯ + 200.00 j¯ - 200.00 k¯

where i¯ , j¯ and k¯ are the unit vectors along with x, y and z axes, respectively.