AP EAPCET 23-Aug-2021 Shift 2 Paper

Since, we know that the equation of plane passing through a point A and perpendicular to vector n is (r−a)n=0
where, a is the position vector of point and n is the normal vector.
Given, A=(2,1−3), n=3

^

i

−

^

j

+2

^

k

⇒a=2

^

i

+

^

j

−3

^

k

and r=x‌hat‌i+y‌hat‌j+z‌hat‌k
∴(r.a).n=0 ⇒3(x−2)−(y−1)+2(z+3)=0
⇒3x−6−y+1+2z+6=0
⇒3x−y+2z+1=0
∵(

1

3

,3,

1

2

) and (1,5,

1

2

) satisfies the above equation.