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JEE Main2017MathematicsThree Dimensional GeometryActual

The coordinates of the foot of the perpendicular from the point 1 , - 2 , 1 on the plane containing the lines x + 1 6 = y - 1 7 = z - 3 8 and x - 1 3 = y - 2 5 = z - 3 7 , is:

Options

  1. A2 , - 4 ,   2
  2. B1 ,   1 ,   1
  3. C0 ,   0 ,   0
  4. D- 1 ,   2 , - 1

Correct answer

C. 0 ,   0 ,   0

Step-by-step solution

Direction ratio's of the plane perpendicular to two given lines is, n → =   n → 1 × n → 2   = i ^ j ^ k ^ 6 7 8 3 5 7 = i ^ 49 - 40 - j ^ 42 - 24 + k ^ 30 - 21 = 9 i ^ - 18 j ^ + 9 k ^ Hence, d r ' s = 9 , - 18 , 9 Now, plane passes through - 1 , 1 ,   3 (A point on the first line), Hence, the equation of plane containing lines is 1 x + 1 - 2 y - 1 + z - 3 = 0 ⇒ x - 2 y + z = 0 ∴ Foot of perpendicular of point 1 , - 2 , 1 is x - 1 1 = y + 2 - 2 = z - 1 1 = &

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