Plane

Chapter 11 Class 12 Three Dimensional Geometry
Serial order wise

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Transcript

Question 1 In each of the following cases, determine the direction cosines of the normal to the plane and the distance from the origin. (d) 5y + 8 = 0 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 the plane is 5y + 8 = 0 5y = β8 β5y = 8 0x β 5y + 0z = 8 0x β 5y + 0z = 8 Comparing with ax + by + cz = d a = 0, b = β5, c = 0 & d = 8 & β(π^2+π^2+π^2 ) = β(0^2 + γ(β5)γ^2 + 0^2 ) = β25 = 5 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 = 0/5, m = (β5)/5, n = ( 0)/5 β΄ Direction cosines of the normal to the plane are = (0, β1, 0) And, Distance form the origin = π/β(π^2 + π^2 + π^2 ) = π/π