Three Dimensional Geometry Part 1

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)

√2√a2+b2+c2

⇒ a2 = –2bc and b = –c
we get a2 = 2c2
⇒ a = ± √2 c
⇒ direction ratio (a, b, c) = (2 , √2 , - √2)