Answer to Question #254728 in Civil and Environmental Engineering for Apple

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 ).(in complete solution)

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