If lines (x - 1)/2 = (y + 1)/3 = (z - 1)/4 and (x - 3)/1 = (y - k)/2 = z/1 intersect each other then find k.

Question

If lines \(\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{4}\) and \(\frac{x - 3}{1} = \frac{y - k}{2} = \frac{z}{1}\) intersect each other then find k.

(x - 1)/2 = (y + 1)/3 = (z - 1)/4 and (x - 3)/1 = (y - k)/2 = z/1

Answer 1

The lines

\(\frac{x - x_1}{l_1} = \frac{y - y_1}{m_1} = \frac{z - z_1}{n_1}\) and \(\frac{x - x_2}{l_2} = \frac{y - y_2}{m_2} = \frac{z - z_2}{n_2}\)

The equations of the given lines are

Since these lines intersect, we get