Discussion
Find the values of k so that the lines
\(\frac{x-2}{2k}=\frac{y-3}{3}=\frac{2+2}{-1}\) and \(\frac{x-2}{8}=\frac{y-3}{6}=\frac{z+2}{-2}\) are parallel.
Answer: B
k = 2.
The direction ratios are the denominators: (2k, 3, -1) for the first line and (8, 6, -2) for the second. (The first line's '2+2' is a misprint for z+2; it does not affect the denominators.) Parallel lines have proportional direction ratios:
\[ \frac{2k}{8} = \frac{3}{6} = \frac{-1}{-2} = \frac{1}{2} \]
so 2k = 4 and k = 2. k = -2 reverses the sign of the first ratio, and 1/2 or 4 make 2k/8 equal to 1/8 or 1, out of proportion with the other two.
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