If the lines $ \frac{x-1}{1}=\frac{y-3}{1}=\frac{z-2}{\lambda} $ and $ \frac{x-1}{\lambda}=\frac{y-3}{2}=\frac{z-4}{1} $ intersect at a point, then the value of $ \lambda^{2}+4 $ is equal to

Question

If the lines $ \frac{x-1}{1}=\frac{y-3}{1}=\frac{z-2}{\lambda} $ and $ \frac{x-1}{\lambda}=\frac{y-3}{2}=\frac{z-4}{1} $ intersect at a point, then the value of $ \lambda^{2}+4 $ is equal to, $ 8 $, $ 10 $, $ 13 $, $ 5 $

MARKS App · Accepted Answer

Both the lines intersect at a point, that means, the vector joining their initial points and the vectors of the lines are coplanar. ⇒ 0 0 2 1 1 λ λ 2 1 = 0 ⇒ 2 2 - λ = 0 ⇒ λ = 2 .

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