Answer is (D) 22y - 9x + z = 35
Equation of any plane containing the line (x - 1)/3 = (y - 2)/1 = z/5 will be
a(x - 1) + b(y - 2) + cz = 0,
where 3a + b + 5c = 0 (1)
It is given that plane passes through (-1, 1, 4). Therefore,
-2a - b + 4c = 0 (2)
From Eqs. (1) and (2), we get
a/-9 = b/22 = c/1
Thus, the equation of required plane is
-9(x - 1) + 22(y - 2) + z = 0
⇒ 22y - 9x + z = 35
