Chapter: 12th Mathematics : UNIT 6 : Applications of Vector Algebra
Condition for coplanarity of two lines
Condition for coplanarity of two lines : (a) Condition in vector form (b) Condition in Cartesian form
Condition for coplanarity of two lines
(a)
Condition in vector form
The two given non-parallel lines 
are coplanar. So they lie in a single plane. Let A and C be the
points whose
position vectors are 
and 
. Then A and C lie on the plane. Since 
and 
are parallel to the plane, × is
perpendicular to the plane. So 
is perpendicular to × . That is,
This is the required condition for coplanarity of two lines in
vector form.
(b)
Condition in Cartesian form
This is the required condition for coplanarity of two lines in
Cartesian form.
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12th Mathematics : UNIT 6 : Applications of Vector Algebra