## lines and planes

1. The problem statement, all variables and given/known data

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

never intersects the line

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

2. Relevant equations

??

3. 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 doesnt work ... help
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 Recognitions: Homework Help Science Advisor 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.