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  4. The value of k such that (x-4/1)=(y-2/1) = (z-k/2) lies in the plane 2x - 4y + z = 7, is

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Q. The value of $k$ such that $ \frac{x-4}{1}=\frac{y-2}{1} = \frac{z-k}{2}$ lies in the plane $2x - 4y + z = 7$, is

IIT JEEIIT JEE 2003Introduction to Three Dimensional Geometry

Solution:

Given equation of straight line
$ \frac{x-4}{1}=\frac{y-2}{1} = \frac{z-k}{2}$
Since, the line lies in the plane $2x - 4y + z = 7$.
Hence, point $(4,2, k)$ must satisfy the plane.
$\Rightarrow 8 - 8 + k = 7 \Rightarrow k = 7 $