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The perpendicular distance of point (1, 1, 3) on the line x2=y+13=−z−3−5\frac{x}{2}=\frac{y+1}{3}=\frac{-z-3}{-5} is

Solution

✅ Correct Option: 4

Rewrite the line as x2=y+13=z+35\frac{x}{2}=\frac{y+1}{3}=\frac{z+3}{5}, with point A(0,−1,−3)A(0,-1,-3) and direction d⃗=(2,3,5)\vec d=(2,3,5). Then AP⃗=(1,2,6)\vec{AP}=(1,2,6), ∣AP⃗∣2=41|\vec{AP}|^2=41, and the projection on d⃗\vec d is 3838=38\frac{38}{\sqrt{38}}=\sqrt{38}. Distance =41−38=3=\sqrt{41-38}=\sqrt3.

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