Three forces `vecF_(1)=(3hati+2hatj-hatk)` dynes, `vecF_(2)=(3hati+4hatj-5hatk)` dynes and `vecF_(3)=a(hati+hatj-hatk)` dynes act simultaneously on a particle. What should be the value of 'a' so that the particle may remain in equilibrium?

Explanation

For equilibrium `vecF_(1)+vecF_(2)+vecF_(3)=vec0rArr3hati+2hatj-hatk+3hati+4hatj-5hatk+ahati+ahatj-ahatk=vec0`
`rArr (6+)ahati+(6+a)hatj-(6+a)hatk=vec0rArr(6+a)(hati+hatj-hatk)=vec0`
As the vector `hati+hatj-hatk` cannot be equal to zero so `6+a=0rArra=-6`