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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

The direction ratios of the normal to the plane passing through the points 1 , - 2 , 3 , - 1 , 2 , - 1 and parallel to the line x - 2 2 = y + 1 3 = z 4 are proportional to

Options

  1. A2 ,   3 ,   4
  2. B4 ,   0 ,   7
  3. C- 2 ,   0 ,   - 1
  4. D2 ,   0 ,   - 1

Correct answer

D. 2 ,   0 ,   - 1

Step-by-step solution

Let, a , b , c be the DRs. The equation of a plane passing through 1 ,   - 2 ,   3 is a x - 1 + b y + 2 + c z - 3 = 0 .... (i) Since, it passes through - 1 ,   2 , - 1   and is parallel to the given line ∴       a - 2 + b 4 + c - 4 = 0 Also, 2 a + 3 b + 4 c = 0 ⇒     a 28 = b 0 = c - 14 ⇒     a 2 = b 0 = c - 1 Hence, a   : b   : c = 2   : 0   :   - 1

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