Answer
$x=2u-3v,y=-1+u+2v,z=5+4u+5v$
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 contains the vectors $\lt 2,1,4\gt$ and $\lt -3,2,5\gt$
and the plane contains the point, whose position vector is $\lt0,-1,5\gt$
Therefore, the vector equation of the plane is
$r(u,v)=\lt0,-1,5\gt+u\lt2,1,4\gt+v\lt-3,2,5\gt$
$r(u,v)=\lt0,-1,5\gt+\lt2u,u,4u\gt+\lt-3v,2v,5v\gt$
This implies
$r(u,v)=\lt2u-3v,-1+u+2v,5+4u+5v\gt$
Hence, the parametric representation of the plane is
$x=2u-3v,y=-1+u+2v,z=5+4u+5v$
