Suppose $\overrightarrow{v}$ and $\overrightarrow{w}$ are two vectors parallel to the plane

$x+2y+3z=7.$

Suppose furthermore that $\overrightarrow{v}$ is perpendicular to $\overrightarrow{w}$ ,

$\Vert v\Vert =3,\text{}\Vert w\Vert =4.$

How would you go about answering this question? I always reach a dead end when I try to solve $\overrightarrow{v}$ and $\overrightarrow{w}$ that satisfy the given information, I just don't know how to go about it. I tried to draw the plane and two parallel vectors, then I know the length of the cross product would be 12. Then what do I do now? How could you solve this to find vectors $\overrightarrow{v}$ and $\overrightarrow{w}$?

$x+2y+3z=7.$

Suppose furthermore that $\overrightarrow{v}$ is perpendicular to $\overrightarrow{w}$ ,

$\Vert v\Vert =3,\text{}\Vert w\Vert =4.$

How would you go about answering this question? I always reach a dead end when I try to solve $\overrightarrow{v}$ and $\overrightarrow{w}$ that satisfy the given information, I just don't know how to go about it. I tried to draw the plane and two parallel vectors, then I know the length of the cross product would be 12. Then what do I do now? How could you solve this to find vectors $\overrightarrow{v}$ and $\overrightarrow{w}$?