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.