Proving Parallelism of Line and Plane in 2x-y+4z=81 and x-2/3=y-3/2=z-1

[fiziksfun]

Homework Statement

show that the plane 2x - y + 4z = 81

never intersects the line

\frac{x-2}{3}=\frac{y-3}{2}=z-1

Homework Equations

??

The Attempt at a Solution

I wanted to show that the line and the plane were parallel. So the unit vector for the line would be 3i + 3j + 1k
RIGHT?
Then I get confused how to show this is parallel to the plane
Planes don't have unit vectors do they ?
The vector normal to the plane i suppose is 2i + -j + 4z

So if the two were parallel a dot b would be = 0
but this doesn't work ... help

 

[Dick]

I think the unit vector of the line is 3i+2j+k. But that doesn't change anything, the direction vector and the normal vector still aren't perpendicular. That can only mean that the line and the plane must intersect. There is probably a typo in the problem.