16
Fig 11 17
© NCERT
not to be republished
 MATHEMATI CS
486
If tr  is the position vector of a point on the line, then
⋅rt n1ˆ
 = d1 and  
⋅rt n2ˆ
 = d2
Therefore, for all real values of λ, we have
1
2
ˆ
ˆ
(
)
t
n
n
⋅
+λ
r
 = 
1
2
d
d
+λ
Since tr is arbitrary, it satisfies for any point on the line Hence, the equation 
1
2
1
2
(
)
r
n
n
d
d
⋅
+ λ
=
+λ
r
r
r
represents a plane π3 which is such
that if any vector rr satisfies both the equations π1 and π2, it also satisfies the equation
π3 i e