Question

A support supplies a force 5 kN to a wall as shown below. What is the x component of the moment (in kN-m) produced by this force about an axis in the direction of i+j+k(from the origin)?

Answer 1

Force is 5 kN

Horizontal Component $i = F_x = 5 cos \theta$

Vertical Component $j =F_y = 5 sin \theta$

 $x$ component of the moment (in kN-m)  $= M = F_x \times d = 5 cos \theta \times d (kN-m)$

$d$ is the distance of the force form origin

Force about an axis in the direction of $i+j+k = F_x + F_y +F_z = 5cos\theta+5sin\theta+0=5(cos\theta+sin\theta)$