Question

Three forces F1, F2 and F3 act at the origin of Cartesian coordinate axes system. The force F1 (= 70N) acts along OA whereas F2 (= 80N) acts along OB and F3 (= 100N) acts along OC. The coordinates of the points A, B and C are (2,1,3), (-1,2,0) and (4,-1,5) respectively. Find the resultant of this force system.

Answer 1

`overline(F1) = 70 [(2i + j+ 3k)/sqrt(2^2 +1^2 +3^2 )] = 37.416i + 18.708j+ 56.12 k`

`overline(F2) = 80 [(-i+2j)/sqrt(-1^2+2^2)] = -35.777 i +71.554j`

`overline(F3 )  100 [(4i - j +5k)/sqrt(4^2+-1^2 +5^2)] = 61.721i - 15.43j +77.152k`

Resultant = `overline F =overline( F1) + overline(F2 )+ overline(F3)` = 37.416 i + 18.708 j + 56.12 k - 35.777 i + 71.554 j 

Resultant = 63.36 i + 74.823 j + 133.272 k

The resultant of the force system = 63.36 i + 74.823 j + 133.272 k