let the magnitude of force applied by each worker be "F"
consider east-west direction along X-axis and north-south direction along Y-axis
In unit vector form, force vector by worker pushing in east direction is given as
[tex]\underset{A}{\rightarrow}[/tex] = F [tex]\hat{i}[/tex] + 0 [tex]\hat{j}[/tex]
In unit vector form, force vector by worker pushing in north direction is given as
[tex]\underset{B}{\rightarrow}[/tex] = 0 [tex]\hat{i}[/tex] + F [tex]\hat{j}[/tex]
resultant force is given as the vector sum of two vector forces as
[tex]\underset{R}{\rightarrow}[/tex] = [tex]\underset{A}{\rightarrow}[/tex] + [tex]\underset{B}{\rightarrow}[/tex]
[tex]\underset{R}{\rightarrow}[/tex] = (F [tex]\hat{i}[/tex] + 0 [tex]\hat{j}[/tex] ) + (0 [tex]\hat{i}[/tex] + F [tex]\hat{j}[/tex] )
[tex]\underset{R}{\rightarrow}[/tex] = F [tex]\hat{i}[/tex] + F [tex]\hat{j}[/tex]
direction of the force is hence given as
θ = tan⁻¹(F/F)
θ = tan⁻¹(1)
θ = 45 degree north of east
hence the direction is north-east
