Answer
$\theta = 100°$
Work Step by Step
We calculate the unit vectors of force 1 and force 2:
$u_{F_1} = \cos 30° \sin30° i + \cos 30° \cos 30°j - \sin 30° k = 0.433i + 0.75j - 0.50k$
$u_{F_2} = \cos 135° i + \cos 60°j + \cos 60° k = 0.707i + 0.50j - 0.50k$
The dot product of the two vectors is:
$u_{F_1} \cdot u_{F_2} = (0.433i + 0.75j - 0.50k) \cdot (0.707i + 0.50j - 0.50k)$
$= (0.433)(-0.707) + (0.75)(0.50) + (-0.50)(0.50) = -0.181$
The angle between the two vectors is:
$\theta = \cos^{-1} (u_{F_1} \cdot u_{F_2}) = \cos^{-1} (-0.181) = 100°$
