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Ex 11.3, 1 - Chapter 11 Class 12 Three Dimensional Geometry - Part 4

Ex 11.3, 1 - Chapter 11 Class 12 Three Dimensional Geometry - Part 5

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Ex 11.3, 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‘Ž/√(π‘Ž^2 + 𝑏^2 +γ€– 𝑐〗^2 ) , m = 𝑏/√(π‘Ž^2 + 𝑏^2 + 𝑐^2 ) , n = 𝑐/√(π‘Ž^2 + 𝑏^2 + 𝑐^2 ) Distance from origin = 𝑑/√(π‘Ž^2 + 𝑏^2 + 𝑐^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 & √(π‘Ž^2+𝑏^2+𝑐^2 ) = √(1^2+1^2+1^2 ) = √3 Direction cosines of the normal to the plane are l = π‘Ž/√(π‘Ž^2 + 𝑏^2 + 𝑐^2 ) , m = 𝑏/√(π‘Ž^2 + 𝑏^2 + 𝑐^2 ) , n = 𝑐/√(π‘Ž^2 + 𝑏^2 + 𝑐^2 ) l = 1/√3 , m = 1/√3, n = 1/√3 ∴ Direction cosines of the normal to the plane are = (𝟏/βˆšπŸ‘, 𝟏/βˆšπŸ‘, 𝟏/βˆšπŸ‘) And, Distance form the origin = 𝑑/√(π‘Ž^2 + 𝑏^2 + 𝑐^2 ) = 𝟏/βˆšπŸ‘

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