Answer
$F = (400~\hat{i}+671~\hat{j})~N$
Work Step by Step
We can find the horizontal component of the force on the beam from the hinge:
$F_x-400~N = 0$
$F_x = 400~N$
We found in part (a) that the gravitational force on the beam is $~~671~N$
We can find the vertical component of the force on the beam from the hinge:
$F_y-mg = 0$
$F_y = mg$
$F_y = 671~N$
We can express the force on the beam from the hinge in unit-vector notation:
$F = (400~\hat{i}+671~\hat{j})~N$
