Question

Find the shortest distance between the lines:
$\frac{x}{5}-\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x+3}{5}-\frac{y-1}{2}=\frac{z+4}{3}$

• A. $3.5$
• B. $4.5$
• C. $5.5$
• D. $6.5$

Answer 1

The correct option is A $3.5$

$\frac{x}{5}-\left(\frac{y-2}{2}\right)=\frac{z-3}{3}$

$\Rightarrow (2x-5y+10)\times 3=10z-30$

$\Rightarrow 6x-15y-10z+60=0⟶\left(1\right)$

$\frac{x+3}{5}-\frac{y-1}{2}=\frac{z+4}{3}$

$\Rightarrow (2x+6-5y+5)\times 3=10z+40$

$\Rightarrow 6x-15y-10z-7=0⟶\left(2\right)$

Parallel distance $=\frac{|-67|}{\sqrt{36+225+100}}=\frac{\left|67\right|}{19}\sim 3.5$ units