Answer
Plane passing through $(0,3,1)$ containing the vectors $\lt 1,0,4\gt$ and $\lt1,-1,5\gt$
Work Step by Step
Given: $r(u,v)=(u+v)i+(3-v)j+(1+4u+5v)k$
The vector equation of a plane containing the vectors $b_{1}$ and $b_{2}$ and containing a point with position vector $a$ is
$r(u,v)=a+ub_{1}+vb_{2}$
Rewrite the given vector equation as follows:
$r(u,v)=(3j+k)+u(i+4k)+v(i-j+5k)$
Therefore, the given vector equation represents a plane passing through $(0,3,1)$ containing the vectors $\lt 1,0,4\gt$ and $\lt1,-1,5\gt$.
