Find the distance of the point P (3, 4, 4) from the point, where the line joining the points A(3, – 4, – 5) and B(2, – 3, 1) intersects the plane 2x + y + z = 7?
Equation of line through the point A (3, – 4, – 5) and B (2, – 3, 1) is
⇒
⇒
Substituting these in the plane equation, We get
2(– r + 3) + (r – 4) + (6r – 5) = 7
⇒ r = 2
⇒ x = 1, y = – 4, z = 7
Distance of (1, – 2, 7) from (3, 4, 4) is
=
= 7