None of the choices represent the vector equation of the given plane.

EDIT:

i) I am sorry for a belated reply, which is due to my not logged to Yahoo answers during these 3 days.

ii) Let the 3 given points be: A(4, 3, 8), B(-6, -6, 2) and C(4, 4, 7)

iii) Let the two lines passing through A be, AB and AC

Vector equation of the line AB is: A + t(B - A)

==> Line AB as: (4, 3, 8) + t(-10, -9, -6) = (4, 3, 8) + t(10, 9, 6)

Similarly line AC as: (4, 3, 8) + s(0, 1, -1)

Thus vector equation of the plane is: (4, 3, 8) + t(10, 9, 6) + s(0, 1, -1)

iv) Similarly with points B and C you can compute the vector equations.

With B it is: (-6, -6, 2) + t(10, 9, 6) + s(10, 10, 5) = (-6, -6, 2) + t(10, 9, 6) + s(2, 2, 1)

With C it is: (4, 4, 7) + t(0, -1, 1) + s(-10, -10, -5) = (4, 4, 7) + t(0, -1, 1) + s(2, 2, 1)

you have to do your own homework