The shortest distance between the lines (x+7)/(-6)=(y-6)/(7)=z and (7-x)/(2)=y-2=z-6 is

3D Geometry: The shortest distance between the lines (x+7)/(-6)=(y-6)/(7)=z and… | JEE Main 2022

JEE Main 2022 (Online) 25th July Evening ShiftQuestion 1

The shortest distance between the lines $\frac{x+7}{-6}=\frac{y-6}{7}=z$ and $\frac{7-x}{2}=y-2=z-6$ is

3D Geometry

$2\sqrt{29}$✓ Correct answer$1$$\sqrt{\frac{37}{29}}$$\frac{\sqrt{29}}{2}$

Solution

Lines: point $(-7,6,0)$, direction $(-6,7,1)$; point $(7,2,6)$, direction $(-2,1,1)$. Cross product: $(7-1,\,-2+6,\,-6+14)=(6,4,8)$, magnitude $\sqrt{116}=2\sqrt{29}$. Connecting vector $(14,-4,6)$: dot $=84-16+48=116$. $SD=\frac{116}{2\sqrt{29}}=2\sqrt{29}$. Option (A).

3D Geometry - JEE Mathematics question (JEE Main 2022 (Online) 25th July Evening Shift)

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