The magnetitude of pairs of displacement vectors are given. Which pairs of displacement vector cannot be added to give a resultant vector of magnitude `13` cm?

Explanation

Angle between the `vec(A)` and `vec(B)=110^(@)-20^(@)=90^(@)`
`R=sqrt(A^(2)+B^(2)+2AB cos 90^(@))=sqrt(5^(2)+12^(2))=13 m`
Let angle of `vec(R)` from `vec(A)` is `alpha`
`tan alpha=(B sin theta)/(A+B cos theta)=(12 sin 90^(@))/(5+12 cos 90^(@))=(12xx1)/(5+12xx0)=12/5`
or `alpha=tan^(-1)(12/5)` with vector `vec(A)` or `(alpha+20^(@))` with X-axis