Answer
$x=u,y=v-u,z=-v$
Work Step by Step
The vector equation of a plane containing the vectors $b_{1}$ and $b_{2}$ and containing a point with position vector $a$ is
$r(u,v)=a+ub_{1}+vb_{2}$
The plane through the origin that contains the vectors $i- j$ and $j-k$
and the plane contains the origin, whose position vector is $0i+0j+0k$
Therefore, the vector equation of the plane is
$r(u,v)=(0i+0j+0k)+u(i-j+0k)+v(0i+j-k)$
$r(u,v)=(0+u+0)i+(0-u+v)j+(0+0-v)k$
This implies
$r(u,v)=ui+(v-u)j-vk$
Hence, the parametric representation of the plane is
$x=u,y=v-u,z=-v$
