Mathematics

Problem

Let

S

be the set of all values of

\lambda

, for which the shortest distance between the lines

\frac{x-\lambda}{0} = \frac{y-3}{4} = \frac{z+6}{1}

and

\frac{x+\lambda}{3} = \frac{y}{-4} = \frac{z-6}{0}

is 13. Then

8 \left| \sum_{\lambda \in S} \lambda \right|

is equal to [April 15, 2023] (a) 304 (b) 308 (c) 306 (d) 302