For shown situation, what will be the magnitude of minimum force in newton that can be applied in any direction so that the resultant force is along east direction?

Explanation

Let force be F so resultant is in east dircection `4hati+ 3hatj+ (5cos 37^(@) hati+ 5sin37^(@)hatj)+ vecF= khati`
`rArr 4hati+3hatj+4hati+3hatj+vecF= khatirArr 8hati+6hatj+ vecF = khati`
`rArr vecF= (k-8)hati-6hatj rArr F = sqrt((k-8)^(2) + (6)^(2)) rArr F_(min)= 6N`
`" "OR" "`
`F_(min)= y`-components of existing forces
`" "= 3N+ 5N sin 37^(@) = 3N + 5N ((3)/(5))= 6N `