finding a base at R3 for the set of vectors in the straight

Finding a base at R3 for the set of vectors in the straight x = 2, y = -2t, z = 31.

If x = 2, y = -2t and z = 3t, then ( x , y, z)^T = ( 2, 0, 0)^T + t ( 0, - 2, 3)^T Also, the vectors ( 2, 0, 0)^T and ( 0, -2, 3)^T are apparently linearly independent. Thus, a basis for R³ is the set containing the vectors ( 2, 0, 0)^T and ( 0, -2, 3)^T .