Consider the vectors
- Find a nonzero vector
perpendicular to both
and
.
- Find a Cartesian equation for the plane through
which is spanned by
and
.
- Find a Cartesian equation for the plane through
which is spanned by
and
.
- Since
and
are independent, we can take
- From part (a) we have
is perpendicular to both
and
, so a Cartesian equation for the plane is given by
Further, since the point
is on the plane, we must have
. Hence, the Cartesian equation for the plane is
- Again, we have a Cartesian equation for the plane given by
Since
is on the plane we must have
Hence, the Cartesian equation for the plane is given by