Ex 11.3

Chapter 11 Class 12 Three Dimensional Geometry
Serial order wise

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### Transcript

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. (a) z = 2 For plane ax + by + cz = d Direction ratios of normal = a, b, c Direction cosines : l = π/β(π^(2 )+ π^2 + π^2 ) , m = π/β(π^2 +γ πγ^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 z = 2 0x + 0y + 1z = 2 Comparing with ax + by + cz = d a = 0, b = 0, c = 1 & d = 2 And, β(π^π+π^π+π^π ) = β(0^2+0^2+1^2 ) = 1 Direction cosines 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 = 0/1 , m = 0/1 , n = 1/1 l = 0, m = 0, n = 1 β΄ Direction cosines of the normal to the plane are = (0, 0, 1) Distance from origin Distance form the origin = π/β(π^2 + π^2 + π^2 ) = 2/1 = 2