Question

Determine: (a) the x, y and z components of the 520 kip force shown below, and (b) the angles $\theta$ ?x, $\theta$ ?y and $\theta$ ?z defining the direction.

Answer 1

Unit vector = [(-5, 10 ,10) - (3, -6 , -6)]/ Magnitude = (-8, 16, 16 ) / (8² + 16² + 16²)^1/2 = (-1/3, 2/3, 2/3)

Components = -520/3 in x direction, 1040/3 in y, 1040/3 in z

Angles = for x = cos-1(-1/3 ) = 70.52 from -negative x axis

for y = cos-1(2/3)= 48.18 from y axis

Similarly for z = 48.18 from z axis