Misc 8 - Chapter 11 Class 12 Three Dimensional Geometry

Transcript

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