Let the direction ratios of the required line be a, b, c. Since the required line is perpendicular to the given lines, therefore,
a + 2b + 3c = 0 ...(i)
and -3a + 2b + 5c = 0 ...(ii)
Solving (i) and (ii), by cross multiplication, we get
Thus, the required line passing through P(-1, 3, - 2) and having the direction ratios a = 4k, b = -14k, c = 8k is
Removing k, we get
which is the required equation of the line.