Answer:
Yes, it lies on the plane
Step-by-step explanation:
Note that the generator (1,2,0) will always make vectors whose third coordinate is always 0. In order to obtain a 4 in the third coordinate, we need to use the generator (0,0,1). Specifically, we need (0,0,1) to be multiplied by 4, if we do that we obtain 4*(0,0,1) = (0,0,4).
We still need to obtain (3,6,4)-(0,0,4) = (3,6,0) from the generator (1,2,0), which is possible because (3,6,0) = 3*(1,2,0). Therefore
3*(1,2,0) + 4 *(0,0,1) = (3,6,4)
Thus, the point (3,6,4) is generated by the two vectors and, as a result, this points lies in the plane.
