If the lines \(\frac{x - 1}{-3} = \frac{y - 2}{2k} = \frac{z - 3}{2}\)

1.	If the lines \(\frac{x - 1}{-3} = \frac{y - 2}{2k} = \frac{z - 3}{2}\) and \(\frac{x - 1}{3} = \frac{y - 1}{1} = \frac{z - 6}{- 5}\)are perpendicular, find the value of k.
Answer» Here Dr’s of the lines are (-3, 2k, 2) and (3k, 1,-5) . since the lines are perpendicular -3 x 3k + 2k x 1 x 2 x -5 = 0 -9k + 2k - 10 = 0 ⇒ - 7k = 10 ⇒ k = \(\frac{-10}{7}\)

If the lines \(\frac{x - 1}{-3} = \frac{y - 2}{2k} = \frac{z - 3}{2}\) and \(\frac{x - 1}{3} = \frac{y - 1}{1} = \frac{z - 6}{- 5}\)are perpendicular, find the value of k.

Answer»

Here Dr’s of the lines are (-3, 2k, 2) and (3k, 1,-5) .

since the lines are perpendicular -3 x 3k + 2k x 1 x 2 x -5 = 0

-9k + 2k - 10 = 0

⇒ - 7k = 10 ⇒ k = \(\frac{-10}{7}\)