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