# 18  Find the distance of the point (– 1, – 5, – 10) from the point of intersection of the line  and the plane   .

Given,

Equation of a line :

Equation of the plane

Let's first find out the point of intersection of line and plane.

putting the value of  into the equation of a plane from the equation from line

Now, from the equation, any  point p  in line is

So the point of intersection is

SO, Now,

The distance between the points (-1,-5,-10) and (2,-1,2) is

Hence the required distance is 13.

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