Plane through a point and parallel to two vectors
There exists exactly one plane parallel to a given pair of non-colinear vectors and passing through a given point.
You can explore that fact in the applet below.
You can control points A, B, C, P either in the edit fields or with a mouse. If you click on a point, four horizontal or two vertical arrows are displayed to indicate whether the point is in the horizontal shift or the vertical shift mode.
The applet displays the equation of the plane in its own (sometimes weird) way. You are welcome to write the equation based on your knowledge to check that your equation is equivalent to the equation provided in the applet window.