JEE Main 2016 · 10 Apr · Shift 1 · Mathematics Q84

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The number of distinct real values of λ for which the lines $\dfrac{x-1}1=\dfrac{y-2}2=\dfrac{z+3}{\lambda^2}$ and $\dfrac{x-3}1=\dfrac{y-2}{\lambda^2}=\dfrac{z-1}2$ are coplanar is :

Answer and worked solution

Official answer: D

Coplanarity needs $\begin{vmatrix}2&0&4\\1&2&\lambda^2\\1&\lambda^2&2\end{vmatrix}=-2\lambda^2(\lambda^2-2)=0$ , so λ = 0 or $\pm\sqrt2$ : three values.

Topics:Skew lines Determinants and properties

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JEE Main 2016 · 10 Apr · Shift 1, Mathematics question 84