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JEE Main2004MathematicsThree Dimensional GeometryActual

A line with direction cosines proportional to 2,1,2 meets each of the lines x=y+a=z and x+a=2 y=2 z . The co-ordinates of each of the point of intersection are given by

Options

  1. A(3 a, 3 a, 3 a),(a, a, a)
  2. B(3 a, 2 a, 3 a),(a, a, a)
  3. C(3 a, 2 a, 3 a),(a, a, 2 a)
  4. D(2 a, 3 a, 3 a),(2 a, a, a)

Correct answer

B. (3 a, 2 a, 3 a),(a, a, a)

Step-by-step solution

Any point on the line x 1 = y+a 1 = z 1 =t₁ (say) is (t₁, t₁-a, t₁ ) and any point on the line x+a 2 = y 1 = z 1 =t₂ ( say ) is (2 t₂-a, t₂, t₂ ) . Now direction cosine of the lines intersecting the above lines is proportional to (2 t₂-a-t₁, t₂-t₁+a, t₂-t₁ ) . Hence 2 t ₂- a - t ₁=2 k , t ₂- t ₁+ a = k and t ₂- t ₁=2 k On solving these, we get t₁=3 a, t₂=a . Hence points are (3 a, 2 a, 3 a) and (a, a, a)

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