Question

The bracket is subjected to the two forces shown. Express each force in Cartesian vector form and then determine the resultant force FR. Given that F2 = 480 N (Figure 1)

Part A  Find the magnitude of the resultant force

Part B  Find coordinate direction angle α of the resultant force 

Answer 1

The important concept here is that if a vector makes an angle with any axis, then the component of the vector along that axis is the cosine of the the magnitude of vector and component perpendicular to the axis is a sine of the magnitude of the vector.

For vector 2, you have all three angles so you can directly get the components.

But for vector 1, you will have to look carefully as you don't have an angle of a vector with all three axes.

Part B