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JEE Main202313 Apr 2023Evening ShiftMathematicsThree Dimensional GeometryActual

The plane, passing through the points ( 0 , – 1 , 2 ) and ( – 1 , 2 , 1 ) and parallel to the line passing through ( 5 , 1 , – 7 ) and ( 1 , – 1 , – 1 ) , also passes through the point

Options

  1. A- 2 ,   5 ,   0
  2. B1 ,   - 2 ,   1
  3. C2 ,   0 ,   1
  4. D0 ,   5 ,   - 2

Correct answer

A. - 2 ,   5 ,   0

Step-by-step solution

Let A 0 , - 1 , 2   &   B - 1 , 2 , 1 and given plane is parallel to line passing through 5 , 1 , - 7   &   1 , - 1 , - 1 So, normal vector to the plane is given by, n → = i ^ j ^ k ^ - 1 - 0 2 + 1 1 - 2 1 - 5 - 1 - 1 - 1 + 7 ⇒ n → = i ^ j ^ k ^ - 1 3 - 1 - 4 - 2 6 = i ^ 16 - j ^ - 10 + k ^ 14 ⇒ n → = 16 i ^ + 10 j ^ + 14 k ^ ∴ Equation of plane 16 ( x   –   0 )   +   10 ( y   +   1 )   +   14   ( z &#

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