Plane

Chapter 11 Class 12 Three Dimensional Geometry
Serial order wise

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Question 1 In each of the following cases, determine the direction cosines of the normal to the plane and the distance from the origin. (b) x + y + z = 1 For plane ax + by + cz = d Direction ratios of normal = a, b, c Direction cosines : l = π/β(π^2 + π^2 +γ πγ^2 ) , m = π/β(π^2 + π^2 + π^2 ) , n = π/β(π^2 + π^2 + π^2 ) Distance from origin = π/β(π^2 + π^2 + π^2 ) Given equation of plane is x + y + z = 1 1x + 1y + 1z = 1 Comparing with ax + by + cz = d a = 1, b = 1, c = 1 & d = 1 & β(π^2+π^2+π^2 ) = β(1^2+1^2+1^2 ) = β3 Direction cosines of the normal to the plane are l = π/β(π^2 + π^2 + π^2 ) , m = π/β(π^2 + π^2 + π^2 ) , n = π/β(π^2 + π^2 + π^2 ) l = 1/β3 , m = 1/β3, n = 1/β3 β΄ Direction cosines of the normal to the plane are = (π/βπ, π/βπ, π/βπ) And, Distance form the origin = π/β(π^2 + π^2 + π^2 ) = π/βπ