Learning Goal: To use the dot product to find the components of forces acting in arbitrary directions. A three-legged structure is shown below. It is attached to the ground at points B = (4.04, 0, 0) and C (-4.04, 0, 0) and connected to the ceiling at point A =(-4.92, 3.79, 4.87). The three legs connect at point D = (0, 3.23, 2.00), where two forces, F and P, act. Force F is given by F 9.60 i 13.5 j + 24.8 k N; P has magnitude 50.0 N and direction angles a = 120.0°, ẞ= 49.0°, and y = 55.6° for the x, y, and z axes, respectively.(Figure 1) Part A - Finding the Cartesian components of a force described by direction angles Find the Cartesian components of force P acting in the x, y, and z directions given P = 50.0 N, a = 120.0°, B=49.0°, and y = 55.6°. Recall that a is the angle between the vector and the x axis, ẞ is the angle between the vector and the y axis, and y is the angle between the vector and the z axis. Express your answers, separated by commas, to three significant figures. ▸ View Available Hint(s) P = 1 ΑΣΦ Η vec ? i N, j N, k N Figure 1 of 1 B F Submit Part B - Finding the angle between forces Find the angle between forces F and P. Express your answer to three significant figures in degrees. ▸ View Available Hint(s) VG ΑΣΦ Η vec Submit ? ° ▾ Part C - Determining the force along a member Determine the magnitude, FDA, acting along member DA, due to the applied force F = 9.60 i - 13.5j+24.8 k N. Express your answer to three significant figures and include the appropriate units.