Find the equation of a line passing through the point P(2, -1, 3) and perpendicular to the lines r = i + j - k + λ(2i - j + k) and r = (2i - j - k) + μ(i + 2j + 2k)

Let the equation of line passing through the point (2, -1, 3) be
x - 2/a = y + 1/b = z - 3/c — (1)
Given lines are
r = (i + j - k) + λ(2i - j + k) — (2)
r = (2i - j - k) + μ(i + 2j + 2k) — (3)
Since (1), (2) and (3) are perpendicular to each other
=> 2a - b + c = 0
a + 2b + 2c = 0
=> a - b = -c
a + 2b = -2c
Solving these equations, we get
a = -4/3c , b = 1/3c , c = c
=> a/(-4) = b/1 = c/3 = l
=> a = -4l, b = l, c = 3l
Putting it in (1) we get required equation of line as
x - 2/-4l = y + 1/l = z - 3/3l
=> x - 2/-4 = y + 1 = z - 3/3