Mathematics Part-II

Book: Mathematics Part-II

Chapter: 11. Three Dimensional Geometry

Subject: Maths - Class 12th

Q. No. 21 of Miscellaneous Exercise

Listen NCERT Audio Books - Kitabein Ab Bolengi

21

Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin, then

Distance of the point (x1,y1,z1) from the plane Ax + By + Cz = D is


The equation of a plane having intercepts a, b, c on the x-, y-, z- axis respectively is



Comparing with Ax + By + Cz = D, we get -


A = 1/a, B = 1/b, C = 1/c, D = 1


Given, the plane is at a distance of 'p' units from the origin.


So, The point is O(0,0,0)


x1 = 0, y1 = 0, z1 = 0


Now,


Distance


Substituting all values, we get -







squaring both sides, we get -



Hence Proved.


21

Chapter Exercises

More Exercise Questions

6

If the lines and are perpendicular, find the value of k.