Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 11.3, 3 Find the Cartesian equation of the following planes: (a) ๐๏ทฏ . ( ๐๏ทฏ + ๐๏ทฏ โ ๐๏ทฏ) = 2 Putting ๐๏ทฏ = x ๐๏ทฏ + y ๐๏ทฏ + z ๐๏ทฏ in equation ๐๏ทฏ.( ๐๏ทฏ + ๐๏ทฏ โ ๐๏ทฏ) = 2 (x ๐๏ทฏ + y ๐๏ทฏ + z ๐๏ทฏ). ( ๐๏ทฏ + ๐๏ทฏ โ ๐๏ทฏ) = 2 (x ร 1) + (y ร 1) + (z ร โ1) = 2 x + y โ z = 2 is the cartesian equation of the given plane. Ex 11.3, 3 Find the Cartesian equation of the following planes: (b) ๐๏ทฏ . (2 ๐๏ทฏ + 3 ๐๏ทฏ โ 4 ๐๏ทฏ) = 1 Putting ๐๏ทฏ = x ๐๏ทฏ + y ๐๏ทฏ + z ๐๏ทฏ in equation ๐๏ทฏ.(2 ๐๏ทฏ + 3 ๐๏ทฏ โ 4 ๐๏ทฏ) = 1 (x ๐๏ทฏ + y ๐๏ทฏ + z ๐๏ทฏ). (2 ๐๏ทฏ + 3 ๐๏ทฏ โ 4 ๐๏ทฏ) = 1 (x ร 2) + (y ร 3) + (z รโ 4) = 1 ๐๐ + 3y โ 4z = 1 Which is the Cartesian equation of the plane. Ex 11.3, 3 Find the Cartesian equation of the following planes: (c) ๐๏ทฏ . [(s โ 2t) ๐๏ทฏ + (3 โ t) ๐๏ทฏ + (2s + t) ๐๏ทฏ] = 15 Putting ๐๏ทฏ = x ๐๏ทฏ + y ๐๏ทฏ + z ๐๏ทฏ in equation ๐๏ทฏ . [(s โ 2t) ๐๏ทฏ + (3 โ t) ๐๏ทฏ + (2s + t) ๐๏ทฏ] = 15 (x ๐๏ทฏ + y ๐๏ทฏ + z ๐๏ทฏ) . [(s โ 2t) ๐๏ทฏ + (3 โ t) ๐๏ทฏ + (2s + t) ๐๏ทฏ] = 15 x (s โ 2t) + y(3 โ t) + z(2s + t) = 15 (s โ 2t) x + (3 โ t) y + (2s + t) z = 15 which is the equation of the plane in Cartesian form.

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.