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JEE MAIN Mathematics QUESTION #975
Question 1
The perpendicular distance of the line \(\dfrac{x-1}{2}=\dfrac{y+2}{-1}=\dfrac{z+3}{2}\) from the point \(P(2,-10,1)\) is:
  • 6
  • \(5\sqrt{2}\)
  • \(4\sqrt{3}\)
  • \(3\sqrt{5}\)✔️
Correct Answer Explanation
Direction vector \(\vec{d}=(2,-1,2)\). Point on line \(A=(1,-2,-3)\). \(\vec{AP}=(1,-8,4)\). \(|\vec{AP}|^2=1+64+16=81\). \(\vec{AP}\cdot\vec{d}=2+8+8=18\). \(|\vec{d}|^2=9\). Distance\(^2=81-\frac{324}{9}=81-36=45\). Distance\(=\sqrt{45}=3\sqrt{5}\).