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For shown situation, what will be the ma...

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?

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The correct Answer is:
6
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`
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