Misc 8 - Find equation of plane passing (a, b, c), parallel - Miscellaneous

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  1. Chapter 11 Class 12 Three Dimensional Geometry
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Misc 8 Find the equation of the plane passing through (a, b, c) and parallel to the plane ๐‘Ÿ๏ทฏ . ( ๐‘–๏ทฏ + ๐‘—๏ทฏ + ๐‘˜๏ทฏ) = 2. The equation of plane passing through (x1, y1, z1) and perpendicular to a line with direction ratios A, B, C is A(x โˆ’ x1) + B (y โˆ’ y1) + C(z โˆ’ z1) = 0 The plane passes through (a, b, c) So, x1 = ๐‘Ž , y1 = ๐‘ , z1 = ๐‘ Since both planes are parallel to each other, their normal will be parallel โˆด Direction ratios of normal = Direction ratios of normal of ๐‘Ÿ๏ทฏ.( ๐‘–๏ทฏ + ๐‘—๏ทฏ + ๐‘˜๏ทฏ) = 2 Direction ratios of normal = 1, 1, 1 โˆด A = 1, B = 1, C = 1 Thus, Equation of plane in Cartesian form is A(x โˆ’ x1) + B (y โˆ’ y1) + C(z โˆ’ z1) = 0 1(x โˆ’ ๐‘Ž) + 1(y โˆ’ b) + 1(z โˆ’ c) = 0 x โˆ’ a + y โˆ’ b + z โˆ’ c = 0 x + y + z โˆ’ (a + b + c) = 0 x + y + z = a + b + c

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