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MathsJEE Main 22 Jan 2026, Shift 1·Q6·MCQ·Moderate

3D Geometry · Shortest distance between skew lines

Let P(α,β,γ)P(\alpha, \beta, \gamma) be the point on the line x−12=y+1−3=z\dfrac{x-1}{2} = \dfrac{y+1}{-3} = z at a distance 4144\sqrt{14} from the point (1,−1,0)(1, -1, 0) and nearer to the origin. Then the shortest distance, between the lines x−α1=y−β2=z−γ3andx+52=y−101=z−31,\frac{x-\alpha}{1} = \frac{y-\beta}{2} = \frac{z-\gamma}{3} \quad\text{and}\quad \frac{x+5}{2} = \frac{y-10}{1} = \frac{z-3}{1}, is equal to
  1. (1)7547\sqrt{\dfrac54}
  2. (2)4754\sqrt{\dfrac75}
  3. (3)4574\sqrt{\dfrac57}
  4. (4)2742\sqrt{\dfrac74}

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