Q10 of 181 Page 1196

Find the distance between the parallel planes x + 2y - 2z + 4 = 0 and x + 2y – 2z – 8 = 0.

Formula : The distance between two parallel planes, say


Plane 1:ax + by + cz + d1 = 0 &


Palne 2:ax + by + cz + d2 = 0 is given by the formula



where () are costants of the planes


Therefore ,


First Plane x + 2y - 2z + 4 = 0 …… (1)


Second plane x + 2y – 2z – 8 = 0 …… (2)


Using equation (1) and (2)


Distance between both planes





More from this chapter

All 181 →
8

Show that the points ( - 3, 0, 1) and (1, 1, 1) are equidistant from the plane 3x + 4y – 12z + 13 = 0.

 9

Find the distance between the parallel planes 2x + 3y + 4 = 4 and 4x + 6y + 8z = 12.

 11

Find the equation of the planes parallel to the plane x – 2y + 2z – 3 = 0, each one of which is at a unit distance from the point (1, 1, 1).

 12

Find the equation of the plane parallel to the plane 2x – 3y + 5z + 7 = 0 and passing through the point (3, 4, - 1). Also, find the distance between the two planes.