Answer to Question #252375 in Civil and Environmental Engineering for karen

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

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

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

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