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JEE Main201910 Jan 2019Morning ShiftMathematicsThree Dimensional GeometryActual

The plane passing through the point ( 4 , - 1 , 2 ) and parallel to the lines x + 2 3 = y - 2 - 1 = z + 1 2 and x - 2 1 = y - 3 2 = z - 4 3 also passes through the point

Options

  1. A1 ,   1 ,   - 1
  2. B- 1 ,   -   1 ,   - 1
  3. C- 1 ,   - 1,   1
  4. D1 , 1 , 1

Correct answer

D. 1 , 1 , 1

Step-by-step solution

Let n → be the normal vector to the plane passing through ( 4 ,   - 1 ,   2 ) and parallel to the given lines, then we know that n → is perpendicular to both the lines. Also, we know that a vector perpendicular to two vectors lie along the cross product of the two vectors. Hence, n → = i ^ j ^ k ^ 3 - 1 2 1 2 3   ⇒ n → = - 7 i ^ - 7 j ^ + 7 k ^ Thus, the direction ratios of the normal to the plane are < - 7 ,   - 7 ,   7 > . The equation of a plane havi

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