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You are given vector vec(A)=5hat(i)-6.5h...

You are given vector `vec(A)=5hat(i)-6.5hat(j)` and `vec(B)=10hat(i)-7hat(j)`.
A third vector `vec(C )` lies in the `x-y` plane. Vector `(C )` is perpendicular to vector `vec(A)` and the scalar product of `vec(C )` with `vec(B)` is 15. From this information, find the component of `vec(C )`

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The correct Answer is:
`y=3/4`, `x=39/40`
Since `vec(C )` lies in x-y plane, let us assume `vec(C )=xhat(i)+yhat(j)`.
Now `vec(C ).vec(A)=orArr5x-6.5y=0`..(i)
and `vec(C ).vec(B)=15rArr10x+7y=15`..(ii)
From Eqs.(i) and (ii),`y=3/4,x=39/40`
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