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Last updated at Feb. 1, 2020 by Teachoo
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Misc 8 Find the equation of the plane passing through (a, b, c) and parallel to the plane ๐ โ . (๐ ฬ + ๐ ฬ + ๐ ฬ) = 2.The equation of plane passing through (x1, y1, z1) and perpendicular to a line with direction ratios A, B, C is A(x โ x1) + B (y โ y1) + C(z โ z1) = 0 The plane passes through (a, b, c) So, x1 = ๐, y1 = ๐, z1 = ๐ Since both planes are parallel to each other, their normal will be parallel โด Direction ratios of normal = Direction ratios of normal of ๐ โ.(๐ ฬ + ๐ ฬ + ๐ ฬ) = 2 Direction ratios of normal = 1, 1, 1 โด A = 1, B = 1, C = 1 Thus, Equation of plane in Cartesian form is A(x โ x1) + B (y โ y1) + C(z โ z1) = 0 1(x โ ๐) + 1(y โ b) + 1(z โ c) = 0 x โ a + y โ b + z โ c = 0 x + y + z โ (a + b + c) = 0 x + y + z = a + b + c โด Direction ratios of normal = Direction ratios of normal of ๐ โ.(๐ ฬ + ๐ ฬ + ๐ ฬ) = 2 Direction ratios of normal = 1, 1, 1 โด A = 1, B = 1, C = 1 Thus, Equation of plane in Cartesian form is A(x โ x1) + B (y โ y1) + C(z โ z1) = 0 1(x โ ๐) + 1(y โ b) + 1(z โ c) = 0 x โ a + y โ b + z โ c = 0 x + y + z โ (a + b + c) = 0 x + y + z = a + b + c
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