Question

The shortest distance between the lines \[ \frac{x - 7}{3} = \frac{y + 4}{-16} = \frac{z - 6}{7} \] and \[ \frac{x - 10}{3} = \frac{y - 30}{8} = \frac{z - 6}{5} \] is

• A. \( \frac{3}{214} \)
• B. \( \frac{4}{173} \)
• C. \( \frac{9}{256} \)
• D. \( \frac{7}{231} \)

Hint:

For non-parallel lines, the shortest distance is given by \( \frac{|(r_1 - r_2) \cdot (b_1 \times b_2)|}{|b_1 \times b_2|} \).

Answer 1

The Correct Option is B

We compute the shortest distance between two skew lines using the formula for the distance between two non-parallel lines.