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AP EAMCET20226 Jul 2022Morning ShiftMathematicsThree Dimensional GeometryActual

If a , b , c are the intercepts made by the plane passing through the point (1,2,3) parallel to the plane 3 x +4 y -5 z =0 on X , Y , Z -axes respectively then 3 a + b +5 c =

Options

  1. A0
  2. B1
  3. C-1
  4. D2

Correct answer

C. -1

Step-by-step solution

Since a,b,c are intercepts made by the plane passin through the point (1,2,3) Let P₁= x a + 4 b + z c =1 Let P₂=3 x+4 y-5 z=0 P ₂ II P ₁ and P ₁ passing the (1,2,3) now P ₁ can be written as aligned & P₁=3(x-1)+4(y-2)-5(z-3)=0 & P₁=3 x+4 y-5 z+4=0 & P₁= x ( -4 3 ) + y (-1) + z ( 4 5 ) =1 aligned on comparing (i) and (iii) aligned & a = -4 3 , ~b =-1, c = 4 5 & 3 a + b +5 c =-1 aligned

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