We have the, straight line given as,

and the plane as,

i.e. x - 5y + z=5 x - 5y + z - 5=0

Let us, check whether the plane and the straight line are parallel using the scalar product between the governing vector of the straight line, , and the normal vector of the plane given as, . If the straight line and the plane are parallel the scalar product will be zero.

=1 - 5 + 4

=0

From the given equation of the line, it is clear that, (2, - 2, 3) is a point on the straight line.

Distance from point (2, - 2, 3) to the plane, will be equal to the distance of the line from the plane.

We know, that the distance of a point (x₀, y₀, z₀) from a plane Ax + By + Cz + D=0 …………… (2) is

On comparing, equation (1) i.e. x - 5y + z - 5=0 with

equation (2) we get,

A=1, B= - 5, C=1, D= - 5.

So, the distance from point (2, - 2, 3) to the plane