\(\mathbf r(t)=t\mathbf i+(6t-t^2)\,\mathbf k=x(t)\mathbf i+y(t)\mathbf j+z(t)\mathbf k\)
\(\implies z=x^2y^2\iff 6t-t^2=t\times0=0\impiles t(6-t)=0\implies t=0,6\)
At \(t=0\), you have \(\mathbf r(0)=0\mathbf i+0\mathbf j+0\mathbf k\).
At \(t=6\), you have \(\mathbf r(6)=6\mathbf i+0\mathbf j+0\mathbf k\).
