The force shown acting at point O has magnitude F 350 lb Th

The force shown acting at point O has magnitude F = 35.0 lb. The direction angle between the force and the x-axis is alpha = 120 degree. The direction angle between the force and the z-axis is gamma = 120 degree. Determine the direction angle in degrees between the force and the y-axis. Express the force as a Cartesian vector in pounds.)

Solution

Fx = F cos(alpha) = 35 cos120 = - 17.5 lb

Fz = F cos(gamma) = 35 cos(120 ) = - 17.5 lb

And |F| = sqrt[ Fx^2 + Fy^2 + Fz^2]

35^2 = 17.5^2 + Fy^2 + 17.5^2

|Fy| = 24.75 lb .........This is the magnitude of Fy.

And as we can see from the figure, Fy will be positive.

Angle between y axis and force, Beta = cos^-1(Fy/F) = cos^-1(24.75/35)

beta = 45 deg .........Ans

F = Fxi + Fy j + Fz k

F = - 17.5 i + 24.75 j - 17.5 k lb