Question #252375

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 )

Expert's answer

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"

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