JEE Main 18 March 2021 Shift 1 Solved Paper

Let P≡(4,−3,1)
and Q≡(2,3,−5)
∴‌‌M=‌

P+Q

2

⇒‌‌M≡(‌

4+2

2

,‌

−3+3

2

,‌

1−5

2

)
⇒‌‌M≡(3,0,−2)
Also, direction ratios of PQ={4−2,−3−3,1+5}
={2,−6,6}
⇒ Direction ratios of PQ={1,−3,3}= direction ratios of normal to the plane.
∴ Equation of the plane is
1(x−3)−3(y−0)+3(z+2)=0
⇒‌‌x−3y+3z+3=0
Comparing this to ax+by+cz+d=0, we get
a=1,b−3,c=3,d=3
∴ Minimum value of (a2+b2+c2+d2)=28