Question

Determine the resultant of the system of concurrent forces having the following magnitudes

and passing through the origin and the indicated points: P = 280 lbs, C ( 6, -4, 0 ); T = 520 lbs, B

( -3, -4, 0 ); F = 270 lbs, D ( 4, 6, 0 ). Point A is located at ( 0, 0, 12 )

Answer 1

Distance

$d = \sqrt{x^2 + y^2 + z^2}$

Components of given forces

$From \space \dfrac{F_x}{x} = \dfrac{F_y}{y} = \dfrac{F_z}{z} = \dfrac{F}{d}$

$F_x = \dfrac{x \, F_x}{d}$ $F_y = \dfrac{y \, F_y}{d}$ $F_z = \dfrac{z \, F_z}{d}$

Resultant

$R = \sqrt{{R_x}^2 + {R_y}^2 + {R_z}^2}$

Direction cosines of the resultant

$\cos \theta_x = \dfrac{R_x}{R} = -0.394$

$\cos \theta_y = \dfrac{R_y}{R} = 0.762$

$\cos \theta_z = \dfrac{R_z}{R} = -0.514$