Question

The shortest distance between the lines
\[\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}\]
and
\[\frac{x-2}{3} = \frac{y-4}{4} = \frac{z-5}{5}\]is:

• A. 1
• B. $\frac{1}{\sqrt{3}}$
• C. $\frac{1}{\sqrt{6}}$
• D. $\frac{1}{2\sqrt{3}}$

Hint:

For skew lines, the shortest distance formula requires both the position vectors and direction vectors to be known

Answer 1

The Correct Option is C

For shortest distance between skew lines, use the formula:
\[d = \frac{|(\vec{b}_1 - \vec{b}_2) \cdot (\vec{d}_1 \times \vec{d}_2)|}{|\vec{d}_1 \times \vec{d}_2|}\]
where a1 and a2 are points on the lines and b1 and b2 are direction vectors of the lines.