A plane can be defined by two vectors if you like (both in the plane, and eg. perpendicular to one another), or by one vector (perpendicular to the plane), or by three points (in the plane, and not on one line), or ...

your ray is defined by (in 3D) :

r = L + t (V - L)

and your plane as :

p = P0 + u(P1 - P0) + v(P2 - P0)

with P0, P1 and P2 the three points that define the plane (not on one line !).

To find where the ray "cuts" the plane :

L + t (V - L) = P0 + u(P1 - P0) + v(P2 - P0)

This can be easily solved for unknowns t, u and v ...

your ray is defined by (in 3D) :

r = L + t (V - L)

and your plane as :

p = P0 + u(P1 - P0) + v(P2 - P0)

with P0, P1 and P2 the three points that define the plane (not on one line !).

To find where the ray "cuts" the plane :

L + t (V - L) = P0 + u(P1 - P0) + v(P2 - P0)

This can be easily solved for unknowns t, u and v ...