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AP EAMCET20225 Jul 2022Evening ShiftMathematicsThree Dimensional GeometryActual

If -2, 4 3 , -4 5 are the intercepts made by a plane on X , Y , Z -axes respectively then the direction cosines of a normal to this plane are

Options

  1. A( -1 3 , 2 3 , -2 3 )
  2. B( 2 3 5 , -4 3 5 , 5 3 5 )
  3. C( -4 57 , 4 57 , -5 57 )
  4. D( 2 38 , -3 38 , 5 38 )

Correct answer

D. ( 2 38 , -3 38 , 5 38 )

Step-by-step solution

If plane makes intercepts a, b, c then equation of plane is x a + y b + z c =1 for -2,4 / 3,-4 / 5 , equation of plane is aligned & x -2 + y ( 4 3 ) = z ( -4 5 ) =1 & x -2 + 3 y 4 - 52 4 =1 & -2 x+3 y-52 4 =1 aligned aligned & -2 x+3 y-52=4 & 2 x-3 y+52+4=0 aligned Direction ratio of normal to plane are (2,-3,5) Direction ratio normal to plane are aligned & ( 2 2^2+3^2+5^2 , -3 2^2+3^2+5^2 , 5 2^2+3^2+5^2 ) & = ( 2 38 , -3 38 , 5 38 ) aligned

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