Hi, can someone check my work please?

1 a) Find the vector and parametric equations of plane containing the points A(4,3,-5), B(-3,1,7) and C(1,2,3).
b) Does the point Q(2,2,1) lie on the plane?

My answers:

1 a) V eqtn
pi: (x,y,z)= (4,3,-5) + s(-7,-2,12) +t(-3,-1,8)
P eqtn
x=4-7s-3t
y=33-2s-t
z=-5+12s+8t

b) no, q is not on the pi

also quick question regarding a) .. my teacher always puts pi: (x,y,z)= ...
why is there a pi in front of the v eqtn? what does it represent or mean? same with part b) why is pi used instead of plane? what's the difference?