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JEE Main2012MathematicsThree Dimensional GeometryActual

A line with positive direction cosines passes through the point P(2,-1,2) and makes equal angles with the coordinate axes. If the line meets the plane 2 x+y+z=9 at point Q , then the length P Q equals

Options

  1. A2
  2. B2
  3. C3
  4. D1

Correct answer

C. 3

Step-by-step solution

Point P is (2,-1,2) Let this line meet at Q(h, k, w) Direction ratio of this line is (h-2, k+1, w-2) Since, d c_s are equal & d r_s are also equal, So, h-2=k+1+w-2 k=h-3 and w=h This line meets the plane 2 x+y+z=9 at Q , so, 2 h+k+w=9 or 2 h+h-3+h=9 4 h-3=9 h=3 and k=0 and w=3 Distance aligned P Q & = (3-2^2 )+ (0-(-1)^2 )+(3-2)^2 & = 1^2+1^2+1^2 = 3 aligned

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