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  4. The plane containing the line (x - 1/1) = (y - 2/2) = (z - 3/3) and parallel to the line (x/1) = (y/1) = (z/4) passes through the point :

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Q. The plane containing the line $\frac{x - 1}{1} = \frac{y - 2}{2} = \frac{z - 3}{3}$ and parallel to the line $\frac{x}{1} = \frac{y}{1} = \frac{z}{4}$ passes through the point :

JEE MainJEE Main 2014Three Dimensional Geometry

Solution:

Normal vector $= \begin{vmatrix}i&j&k\\ 1&2&3\\ 1&1&4\end{vmatrix} = 5i-\hat{j} - \hat{k}$
point $\left(1,2,3\right)$ lies in plane so equation of
plane $= 5 \left(x - 1\right) - 1 \left(y - 2\right) - 1 \left(z - 3\right) = 0$
$5x - y - z = 0$
so option $\left[2\right]$ is correct