Three Dimensional Geometry Part 2

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=

1

2

Coordinate of Q is (

1

2

,0,

−1

2

)
⇒PQ=√(−1−

1

2

)2+(2−0)2+(−2+

1

2

)2
=√

9

4

+4+

9

4

=

√34

2