The correct option is A √2,1,−1
BONUS QUESTION : Two options are correct.
Direction of ratios of line through A(0,−1,0) and B(0,0,1) is (0,1,1)
Let DR's of normal to plane be (a,b,c)
∴b+c=0
cosπ4=a(0)+b(1)+c(−1)√a2+b2+c2√(1)2+(−1)2
⇒1√2=b−c√a2+b2+c2×√2
⇒a2+b2+c2=b2+c2−2bc
⇒a2=−2bc
⇒a2=−2b(−b)
⇒a2=2b2
⇒a=√2b
∴ DR's of normal to plane are (√2,−1,1) or (√2,1,−1) or any multiple of it.
So, (2,√2,−√2) is also correct.