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?

Answer

6

Explanation

Let force be F so resultant is in direction
`4hat(i)+3hat(j)+(5 cos 37^(@) hat(i)+5 sin 37^(@) hat(j))+vec(F)=khat(i)`
`rArr 4hat(i)+3hat(j)+4hat(i)+3hat(j)+vec(F)=khat(i) rArr 8hat(i)+6hat(j)+vec(F)=khat(i)`
`rArr vec(F)=(k-8) hat(i)-6hat(j) rArr F=sqrt((k-8)^(2)+(6)^(2)) rArr F_(min)=6N`