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  4. The distance of the point (7,-3,-4) from the plane passing through the points (2,-3,1),(-1,1,-2) and (3,-4,2) is :

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Q. The distance of the point $(7,-3,-4)$ from the plane passing through the points $(2,-3,1),(-1,1,-2)$ and $(3,-4,2)$ is :

JEE MainJEE Main 2023Three Dimensional Geometry

Solution:

$=\begin{vmatrix} x-2 & y+3 & z-1 \\ -3 & 4 & -3 \\ 4 & -5 & 4 \end{vmatrix}=0$
$x-z-1=0$
Distance of $P (7,-3,-4)$ from Plane is
$d =\left|\frac{7+4-1}{\sqrt{2}}\right|=5 \sqrt{2}$