Determine the magnitude of the projection of the force F1 al

Determine the magnitude of the projection of the force F1 along cable AC. Suppose that a = 2 m and b = 5 m . (Figure 1)

Express your answer to three significant figures and include the appropriate units.

vector AB = B -A = (0, 2, 0) - (2, -2, 3) = -2i + 4j - 3k

F1 is along AB.

so ABcap ( unit vector) = -2i + 4j - 3k / (sqrt(2^2 + 4^2 + 3^2)

= -2i + 4j - 3k / 5.39

so F1 will be : vectorF1 = 70 Abcap = 70 ( -2i + 4j - 3k) / 5.39

AC = C - A = (-2, 2, 5) - (2, -2, 3) = -4i + 4j + 2k

ACcap = -4i + 4j + 2k / (sqrt(4^2 + 4^2 + 2^2) = (-4i + 4j + 2k )/ 6

projetion of F1 along AC

= F1.ACcap = (70 ( -2i + 4j - 3k) / 5.39 ) .( -4i + 4j + 2k )/ 6

= 70 (8 + 16 -6) / (5.39 x 6) = 38.96 N ...........Ans