Two couples are applied to a triangular prism as shown below. The dashed lines in the gure represent lines along the inclined surface of the prism. Determine the resultant couple-moment vector. Also, determine the magnitude of the resultant couple-moment, its unit vector, and the angles it makes with x, y, and z axes. U L /\\l A 450 mm 250 mm \\73 \\ A hexagonal mat foundation supports four column loads as shown below. The hexagon has side lengths of 10 feet and its interior angles are 120 degrees. Determine the magnitudes of the additional loads that must be applied at B and F for the resultant of all six loads to pass through the center of the mat (point 0)