Subscribe to our Youtube Channel - https://www.youtube.com/channel/UCZBx269Tl5Os5NHlSbVX4Kg
Example 15 - Chapter 11 Class 12 Three Dimensional Geometry
Last updated at May 29, 2018 by Teachoo
Transcript
Example 15 (Method 1) Find the distance of the plane 2x 3y + 4z 6 = 0 from the origin. Given, the equation of plane is 2x 3y + 4z 6 = 0 2x 3y + 4z = 6 Direction ratios of = , , a = 2, b = 3, c = 4 Also, 2 + 2 + 2 = 2 2 + ( 3) 2 + 4 2 = 4+9+16 = 29 Direction cosines are l = 2 + 2 + 2 , m = 2 + 2 + 2 , n = 2 + 2 + 2 l = 2 29 , m = 3 29 ,n = 4 29 Equation of plane is lx + my + nz = d 2 29 x 3 29 y + 4 29 z = d 2x 3y + 4z = d 29 Comparing with (1) i.e. 2x 3y + 4z = 6, d 29 = 6 d = Example 15 (Method 2) Find the distance of the plane 2x 3y + 4z 6 = 0 from the origin. Distance of point P(x1, y1, z1) from plane Ax + By + Cz = D is d = 1 + 1 + 1 2 + 2 + 2 Since we have to find distance from Origin P(x1, y1, z1) = O(0, 0, 0) x1 = 0, y1 = 0, z1 = 0 & plane is 2x 3y + 4z 6 = 0 2x 3y + 4z = 6 Comparing with Ax + By + Cz = D A = 2, B = 3, C = 4 & D = 6 Putting values in formula d = 1 + 1 + 1 2 + 2 + 2 d = 2 0 3 0 + 4 0 6 2 2 + ( 3) 2 + 4 2 d = 6 4 + 9 + 16 d = 6 29 d =
Examples
Example 1
Example, 2 Important
Example, 3
Example, 4 Important
Example, 5 Important
Example, 6 Important
Example, 7
Example 8
Example, 9
Example 10
Example 11
Example 12 Important
Example 13 Important
Example 14
Example 15 You are here
Example 16 Important
Example 17
Example 18
Example 19 Important
Example 20 Important
Example 21 Important
Example 22
Example 23 Important
Example 24
Example, 25 Important
Example 26
Example 27 Important
Example 28 Important
Example 29 Important
Example 30 Important
Chapter 11 Class 12 Three Dimensional Geometry
Serial order wise
About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.