Example 15
Last updated at Dec. 8, 2016 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 𝑛 = 𝑎, 𝑏, 𝑐 a = 2, b = −3, c = 4 Also, 𝑎2+ 𝑏2+ 𝑐2 = 22 + (− 3)2 + 42 = 4+9+16 = 29 ∴ Direction cosines are l = 𝑎 𝑎2 + 𝑏2 + 𝑐2 , m = 𝑏 𝑎2 + 𝑏2 + 𝑐2 , n = 𝑐 𝑎2 + 𝑏2 + 𝑐2 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 = 𝟔 𝟐𝟗 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 = 𝐴 𝑥1 + 𝐵 𝑦1 + 𝐶 𝑧1 − 𝐷 𝐴2 + 𝐵2 + 𝐶2 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 = 𝐴 𝑥1 + 𝐵 𝑦1 + 𝐶 𝑧1 − 𝐷 𝐴2 + 𝐵2 + 𝐶2 d = 2 0 − 3 0 + 4 0 − 6 22 + (−3)2 + 42 d = −6 4 + 9 + 16 d = −6 29 d = 𝟔 𝟐𝟗
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Chapter 11 Class 12 Three Dimensional Geometry
Serial order wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.