Let L be the line of intersection of 2x+3y+2z=0 and x−2y+z=0 If z=0, then x=y=0 The line L is parallel to r1×r2, where r1=2
^
i
+3
^
j
+2
^
k
and r2=
^
i
−2
^
j
+
^
k
|
^
i
^
j
^
k
2
3
2
1
−2
1
|=7
^
i
−7
^
k
DR's of is (1,0,−1) and equation of L is
x
1
=
y
0
=
z
−1
=λ
Let PQ be the distance from the point P(−1,2,−2) to the line L. DRs of PQ=λ+1,−2,2−λ ∴ PQ ⊥ r ⇒(λ+1)(1)+(−2)(0)+(2−λ)(−1)=0 ⇒λ+1−2+λ=0 ⇒λ=