AP EAPCET 20-Aug-2021 Shift 2 Paper

Given that, equation of plane parallel to vectors 2

^

i

+

^

j

+

^

k

and

^

i

−

^

j

+

^

k

. Also, it passes through 3

^

i

+2

^

j

+6

^

k

.
Let the plane be a(x−3)+b(y−2)+c(z−6)=0 ...(i)
such that,
a(2)+b(1)+c(1)=0
⇒2a+b+c=0 ...(ii)
and a(1)+b(−1)+c(1)=0
⇒a−b+c=0 ...(iii)
From Eq. (ii) and (iii)
⇒

a

2

=

b

−1

=

c

−3

=λ ...(say)
⇒a=2λ,b=−λ,c=−3λ
From Eq. (i), we get
2λ(x−3)−λ(y−4)−3λ(z−6)=0
⇒4x−3−(y−4−3(z−6)=0
⇒2x−y−3z=−14