Is the line parallel to the plane?

[cyt91]

Is the line x=1-2t,y=2+5t,z=-3t parallel to the plane 2x+y-z=8?

I've used the approach of finding the dot product of the directional vector of the line and the vector normal to the plane in this question. The line is not parallel to the plane.
But I'm not too sure if my working is correct. Can anyone please check my working?

It's here:

https://skydrive.live.com/?cid=6b04...751C72E14AD&id=6B041751C72E14AD!160&sc=photos

Thank you.

 

[ehild]

It is correct. But you need to write a sentence for explanation, that if it was parallel with the plane than it would be perpendicular to the normal vector of the plane.

ehild

 

[cyt91]

Ok. Thanks.

 

[Bacle]

Also, if the line were not parallel to the plane, it would intersect the plane at some point in the plane. Does it?