Three forces act at point O, the origin ofcoordinates. F1 = (2 i 13 j + 22 k)kN

Question

Three forces act at point O, the origin ofcoordinates. F1 = (2i 13j + 22k)kN , F2 =(2i +10j + 5k)kN ,
F3 = [(F3x)i + (F3y)j +(F3z)k]kN .

Knowing that the resultant R = F1+ F2 + F3is directed vertically upward ( R = R zk ) with magnitudeof15kN , determine the direction anglesof F3 . please show how you got any of theconclusions and what steps you took. thank you Three forces act at point O, the origin ofcoordinates. F1 = (2i 13j + 22k)kN , F1 = (2i 13j + 22k)kN , F2 =(2i +10j + 5k)kN ,
F3 = [(F3x)i + (F3y)j +(F3z)k]kN .

Knowing that the resultant R = F1+ F2 + F3is directed vertically upward ( R = R zk ) with magnitudeof15kN , determine the direction anglesof F3 . please show how you got any of theconclusions and what steps you took. thank you

Explanation / Answer

F1 = (2i 13j + 22k)kN , F2 = (2i +10 j + 5k) kN ,
F3 = [(F3x)i + (F3y )j + (F3z)k]kN.
R = Rz k = 15 k
(2i 13j + 22k)+ (2i +10 j + 5k) + (F3x)i + (F3y )j + (F3z)k =15 k
F3x = 4,F3y = 3,F3z = -12
magnitude of F3 = (42 +32 + 122) = 13
thedirection angles of F3 are
= cos-1(F3x /F3) =72.1o
=cos-1(F3y /F3) = 76.7o
= cos-1(F3z /F3) =157.4o

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