The dr’s of a normal to the plane through (1,0,0), (0,1,0) which makes an angle of π4 with the plane x+y=3 are

Any plane through (1,0,0) is A(x−1)+B(y−0)+C(z−0)=0  .......(1)It contains (0,1,0) if −A+B=0......(2)Also (1) makes an angle of  π4 with the plane x+y=3∴cosπ4=|A+B|A2+B2+C2 12+12⇒2AB=C2………(3)From (2) and (3), C2=2A2⇒C=±2AHence A:B:C =A:A: ±2.AD.r's are (1,1, ±2)