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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