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  4. The points, whose position vectors are 60 i + 3 j, 40i - 8j and ai - 52j collinear, if

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Q. The points, whose position vectors are $60\, i + 3\, j$, $40i - 8j$ and $ai - 52j$ collinear, if

UPSEEUPSEE 2013

Solution:

$(40 i -8 j )-(60 i +3 j )=\lambda[(a i -52 j )-(40 i-8 j)]$
For some scalar $\lambda$,
$-20=\lambda(a-40)$ and $-11=-44 \lambda$
$\Rightarrow \, a-40=\frac{-20}{\lambda}$ and $\lambda=\frac{1}{4}$
$\Rightarrow \, a=40-\frac{20}{1} \times 4=-40$