The direction ratios of normal to the plane through the points (0, -1, 0) and (0, 0, 1) and making an angle π/4 with the plane y - z + 5 = 0 is?

Let the equation of plane be a(x - 0) + b(y + 1) + c(z - 0) = 0
It passes through (0, 0, 1) then b + c = 0 (1)
Now cos(π/4) = a(0) + b(1) + c(-1) / √(a² + b² + c²) => 1/√2 = (b - c) / √(a² + b² + c²)
=> a² = 2c² and b = -c
we get a² = 2c² => a = ±√2c
Direction ratio (a, b, c) = (√2, -1, 1) or (-√2, 1, -1)