Problem Four

$A(0,0,0)$

$B(0,0,5)$

$C(0,8,5)$

$D(-4,8,4)$

Dimensions are in meters. The green force vector has a magnitude of $10$ N and is located in the $1$ st octant with a projection angle, theta, $53$ degrees; a planar angle referenced from the $x-$axis, of $30$ degrees. The orange force vector has a magnitude of $20$ N and has direction cosines, alpha and beta, of $143$ degrees and $60$ degrees. The $z-$component of the orange force vector is negative.

Treat point B as a fixed support. Determine the reactions at point B$.$

Project the green vector onto the line of action of the orange vector and determine the parallel projection.

Determine the CVF of the perpendicular component.

Determine the combined force along the line of action of the orange vector.