EAMCET Engineering 2003 Solved Paper

Let the equation of plane passing through (1,1,1) is
a(x−1)+b(y−1)+c(z−1)=0 . . . (i)
It is also passing through (1,−1,−1).
∴‌‌a(0)+b(−2)+c(−2)‌=0
‌ or ‌b+c‌=0 . . . (ii)
Since, Eq. (i) is perpendicular to the plane
‌∴‌2x−y+z+5‌=0
‌2a−b+c‌=0 . . . (iii)
Since, Eqs. (ii) and (iii) are identical
∴‌‌‌

a

−2−2

=‌

b

−4−0

=‌

c

4

⇒‌

a

−4

=‌

b

−4

=‌

c

4

∴ Required equation of plane is
x+y−z−1=0