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99 Percentile Qs Bank for JEE MainMathematicsThree Dimensional Geometry

A line passing through A   ( 1 ,   2 ,   3 ) and having direction ratios ( 3 ,   4 ,   5 ) meets a plane x   +   2 y   –   3 z   =   5 at B , then distance A B is equal to -

Options

  1. A9 4
  2. B1 1 4
  3. C1 3 4
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

The equation of line L 1 passing through A 1 ,   2 ,   3 and having direction ratios 3 ,   4 ,   5 is given as L 1 : x - 1 3 = y - 2 4 = z - 3 5 = λ   say Any general point on line L 1 is given as 3 λ + 1 ,   4 λ + 2 ,   5 λ + 3 So, co-ordinate of point B is 3 λ + 1 ,   4 λ + 2 ,   5 λ + 3 Since, point B also lies on the given plane x + 2 y - 3 z = 5 Therefore, 3 λ + 1 + 2 4 λ + 2 - 3 5 λ + 3 = 5 ⇒ - 4 λ = 9 &#

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