Manipal Entrance Test 2020 Math Paper

Equation of plane passing through (−1,1,1) is
Also, it is passing through (1,−1,1)
⇒‌‌2a−2b+0c=0
Also, required equation of plane (i) is perpendicular to x+2y+2z=5.
∴‌‌a×1+b×2+c×2=0
∴‌‌a×1+b×2+c×2=0
⇒‌‌a+2b+2c=0
Eqs. (ii) and (iii) are identical.
∴‌‌‌

a

−4−0

=‌

−b

4−0

=‌

c

4+2

⇒‌‌‌

a

−4

=‌

b

−4

=‌

c

6

⇒‌‌‌

a

−2

=‌

b

−2

=‌

c

3

=λ (Say)
⇒‌‌a=−2λ,b=−2λ,c=3λ
On putting the values of a,b and c in Eq. (i), we get
⇒‌‌−2x−2y+3z−3=0
⇒‌‌2x+2y−3z+3=0