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Ex 11.3, 3 - Class 12th - Find Cartesian equation of planes - Equation of plane - In Normal Form

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  1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise
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Ex 11.3, 3 Find the Cartesian equation of the following planes: (a) ๐‘Ÿ๏ทฏ . ( ๐‘–๏ทฏ + ๐‘—๏ทฏ โˆ’ ๐‘˜๏ทฏ) = 2 Putting ๐’“๏ทฏ = x ๐’Š๏ทฏ + y ๐’‹๏ทฏ + z ๐’Œ๏ทฏ in equation ๐‘Ÿ๏ทฏ.( ๐‘–๏ทฏ + ๐‘—๏ทฏ โˆ’ ๐‘˜๏ทฏ) = 2 (x ๐‘–๏ทฏ + y ๐‘—๏ทฏ + z ๐‘˜๏ทฏ). ( ๐‘–๏ทฏ + ๐‘—๏ทฏ โˆ’ ๐‘˜๏ทฏ) = 2 (x ร— 1) + (y ร— 1) + (z ร— โˆ’1) = 2 x + y โˆ’ z = 2 is the cartesian equation of the given plane. Ex 11.3, 3 Find the Cartesian equation of the following planes: (b) ๐‘Ÿ๏ทฏ . (2 ๐‘–๏ทฏ + 3 ๐‘—๏ทฏ โ€“ 4 ๐‘˜๏ทฏ) = 1 Putting ๐’“๏ทฏ = x ๐’Š๏ทฏ + y ๐’‹๏ทฏ + z ๐’Œ๏ทฏ in equation ๐‘Ÿ๏ทฏ.(2 ๐‘–๏ทฏ + 3 ๐‘—๏ทฏ โˆ’ 4 ๐‘˜๏ทฏ) = 1 (x ๐‘–๏ทฏ + y ๐‘—๏ทฏ + z ๐‘˜๏ทฏ). (2 ๐‘–๏ทฏ + 3 ๐‘—๏ทฏ โˆ’ 4 ๐‘˜๏ทฏ) = 1 (x ร— 2) + (y ร— 3) + (z ร—โˆ’ 4) = 1 ๐Ÿ๐’™ + 3y โˆ’ 4z = 1 Which is the Cartesian equation of the plane. Ex 11.3, 3 Find the Cartesian equation of the following planes: (c) ๐‘Ÿ๏ทฏ . [(s โ€“ 2t) ๐‘–๏ทฏ + (3 โ€“ t) ๐‘—๏ทฏ + (2s + t) ๐‘˜๏ทฏ] = 15 Putting ๐’“๏ทฏ = x ๐’Š๏ทฏ + y ๐’‹๏ทฏ + z ๐’Œ๏ทฏ in equation ๐‘Ÿ๏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 โˆ’ t) + z(2s + t) = 15 (s โ€“ 2t) x + (3 โˆ’ t) y + (2s + t) z = 15 which is the equation of the plane in Cartesian form.

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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.
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