The aligned vector with the line is,

The normal vector with the plane is,

.

Now think about this....

A line and plane are parallel implies that the aligned vector is perpendicular (orthogonal) to the normal vector.

To check this we look at the dot product whichis notzero. Thus, theyare notparallel.

Substitute those values of x,y,z into the equation of plane.b) Find the intersection of the line and the plane.

Thus,

.

Thus,