Question

If the points (1, 1, p) and (−3, 0, 1) be equidistant from the plane vector r.(3i+4j 12k)+13=0 ,then find the value of p.

Answer 1

It is known that the perpendicular distance between a point whose position vector is

Similarly, the distance between the point (−3, 0, 1) and the given plane is

It is given that the distance between the required plane and the points, (1, 1, p) and (−3, 0, 1), is equal.