Find a vector-parametric equation of a plane that contains the point (4,-2,14) and is parallel to the vectors u=2i-4j+7k and v=3i+5j-2K.
Vector Parametric Equation of a Plane: r=a+λu+μv
(if u and v are two non-parallel vectors in the plane)
The Attempt at a Solution
If u and v are parallel to the vector, then wouldn't one of the vectors need to be altered in order for the equation to work? If so, I found the cross product of u and v
u x v= -27i+25j+22k
But would that work? I am unsure whether it is necessary to change u and v in the first place, because I don't know if the vectors can't be parallel to each other, the unfound vector, or the plane itself. Does anyone know how this can be found?