Solution Let 
ˆ
ˆ
ˆ
2
5
3
a
i
j
r= + −k
, 
ˆ
ˆ
ˆ
2
3
5
b
i
j
k
= −
−
+
r
, 
ˆ
ˆ
ˆ
5
3
3
c
i
j
= + −k
r
Then the vector equation of the plane passing through ar , b
r
 and crand  is
given by
(
) (RS RT)
r
−a
⋅
×
uuur uuur
r
r
 = 0     (Why )
or
(
) [(
) (
)]
r
a
b
a
c
a
−
⋅
−
×
−
r
r
r
r
r
r
 = 0
i e ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
[
(2
5
3 )] [( 4
8
8 )
(3
2 )]
0
r
i
j
k
i
j
k
i
j
− + − ⋅ − − + × − =
r
R 
S  
T
© NCERT
not to be republished
THREE D IMENSIONAL G EOMETRY
485
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