The two given lines pass through the point having position vector a=
∧
i
+
∧
j
and are parallel to the vectors b1=
∧
i
+2
∧
j
−
∧
k
and b2=−
∧
i
+
∧
j
−2
∧
k
respectively. Therefore, the plane containing the given lines also passes through the point with position vector a=
∧
i
+
∧
j
. Since, the plane contains the lines which are parallel to the vectors b1 and b2 respectivley. Therefore, the plane is normal to the vector n given by. n=b1×b2=|
∧
i
∧
j
∧
k
1
2
−1
−1
1
−2
|
=
∧
i
(−4+1)−
∧
j
(−2−1)+
∧
k
(1+2)
=−3
∧
i
+3
∧
j
+3
∧
k
Thus, the vector equation of the required plane is r⋅n=a⋅n