Does the line lie in the plane?

[The Subject]

Homework Statement

Does the line through the point P(1, 2, 3) with direction vector d = (1, 2, -3) lie in the plane 2x+y-z=3?

Homework Equations

The Attempt at a Solution

From the 2x+y-z i can get the vector (2, 1, -3) and the direction vector, their dot product does not equal zero. So, no it does lie on the plane. Just wondering if my intuition is correct.

 

[LCKurtz]

Yes because, as you might have added, $\langle 2,1,3\rangle$ is perpendicular to the plane. Or you might have noticed that P isn't in the plane in the first place.