To know whether a vector is in a plane, 2 points on the vector must also be in the plane. You could choose any 2 points to check. It really doesn’t matter.
The general equation for a plane is:
a*x+b*y+c*z=d
The vector may have its origin at (1,0) and its top of the arrow at (4,4) where the cakes in parentheses are (x,y). (x,y) could also be (y,z) or (x,z), etc.
simply check whether the pints of the vector can be put into the plane equation and still remain true. Note, however that if the points are being used lack z, or x or y, then that variable should be set to zero within the plane equation while checking whether the filler in variables remain true.
best wishes,
Pharmacoengineering.com