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AP EAMCET20224 Jul 2022Evening ShiftMathematicsThree Dimensional GeometryActual

If the equation of the plane passing through the point A - 2 , 1 , 3 and perpendicular to the vector 3 i ¯ + j ¯ + 5 k ¯ is a x + b y + c z + d = 0 then a + b c + d =

Options

  1. A4 5
  2. B2 3
  3. C1
  4. D- 4 5

Correct answer

D. - 4 5

Step-by-step solution

Given, The plane passes through - 2 , 1 , 3 and is perpendicular to vector 3 i ^ + j ^ + 5 k ^ ∴ Equation of plane is 3 x + y + 5 z = λ passes through - 2 , 1 , 3 So, 3 x + y + 5 z = λ passes through - 2 , 1 , 3 ∴ 3 × - 2 + 1 + 5 × 3 = λ ⇒ - 6 + 1 + 15 = λ ⇒ 10 = λ ∴ Equation of plane is 3 x + y + 5 z = 10 Now on comparing with a x + b y + c z + d = 0 We get a = 3 ,   b = 1 ,   c = 5   &   d = - 10 , So the value of a + b c + d

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