Hello, kingkaisai2!

Find the equation of the plane which passes through the point and which is

parallel to the plane containing the point and the line

To write the equation of a plane, we need a point and its normal direction:

. . Then the equation is: .

We have a point , so we need the normal vector:

Since this plane is parallel to the plane containing point and line ,

. . it has thesamenormal vector.

The line has parametric equations: .

For , we have the point:

For , we have the point:

Hence, the plane contains points:

The normal vector is perpendicular to and

Since and

. .

So the desired plane has point and normal

Can you finish it now?