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JEE Main202529 Jan 2025Evening ShiftMathematicsThree Dimensional GeometryActual

Let a straight line L pass through the point P(2,-1,3) and be perpendicular to the lines x-1 2 = y+1 1 = z-3 -2 and x-3 1 = y-2 3 = z+2 4 . If the line L intersects the y z -plane at the point Q , then the distance between the points P and Q is :

Options

  1. A10
  2. B2 3
  3. C2
  4. D3

Correct answer

D. 3

Step-by-step solution

Vector parallel to L aligned & = | array ccc i & j & k 2 & 1 & -2 1 & 3 & 4 array |=10 i -10 j +5 k & =5(2 i -2 j + k ) aligned Equation of ' L ' x-2 2 = y+1 -2 = z-3 1 = ( say ) Let Q(2 +2,-2 -1, +3) aligned & 2 +2=0 =-1 & Q(0,1,2) & d(P, Q)=3 aligned

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