COMEDK · Maths · 34. Three Dimensional Geometry
The distance of the point \((2,3,4)\) from the line \(1-x=\dfrac{y}{2}=\dfrac{1}{3}(1+z)\) is
- A \(\dfrac{2}{7} \sqrt{35}\)
- B \(\dfrac{1}{7} \sqrt{35}\)
- C \(\dfrac{3}{7} \sqrt{35}\)
- D \(\dfrac{4}{7} \sqrt{35}\)
Answer & Solution
Correct Answer
(C) \(\dfrac{3}{7} \sqrt{35}\)
Step-by-step Solution
Detailed explanation
The given line equation is \(1-x = \dfrac{y}{2} = \dfrac{1+z}{3}\). Rewriting this in standard symmetric form \(\dfrac{x-x_1}{a} = \dfrac{y-y_1}{b} = \dfrac{z-z_1}{c}\), we get \(\dfrac{x-1}{-1} = \dfrac{y-0}{2} = \dfrac{z-(-1)}{3}\). Let the point on the line be…
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