The force P has a magnitude of 50 lb and acts within the oct

The force P has a magnitude of 50 lb and acts within the octant shown. (Figure 1) Determine the magnitudes of the x, y, z components of F using scalar notation. Express your answers using three significant figures separated by a comma.

Solution

|F| ²= |F_x|²+ |Fy|²+ |Fz|²

|Fx| = |F|cos, |Fy| = |F|cos, |Fz| = |F|cos

cos² + cos² + cos² = 1

cos² = cos²60° = 1/4, cos² = cos²45° = 1/2

cos² = 1/4, cos = 1/2, = 60°

|Fx| = |F|cos = 50 x (1/2) = 25 lb

|Fy| = |F|cos = 50 x (0.707) = 35.36 lb

|Fz| = |F|cos = 50 x (1/2) = 25 lb