Vectors - vector equations

Okay, I'm a bit confused here, hoping someone can help clear this up.

The question is "Points A, B and C have co-ords (0, 5), (9, 8) and (4, 3) respectively.
a) Find the vector equation for the line joining A and B.
b) Show that the perpendicular distance from C to line AB is 10^1/2 "

I understand the vector equation = a + t(b - a), which works out for me as:
(0, 5) + t(9, 3)
But the answer at the back of the book says (0, 5) + t(3, 1)

I'll be able to answer b) once I know how it works out at the above answer.
Any help is appreciated

$\begin{pmatrix} 9 \\ 3 \end{pmatrix}$ is the direction vector, it can be simplified as $\begin{pmatrix} 3 \\ 1 \end{pmatrix}$

It is similar to the gradient, if gradient $= \dfrac64$, this means moving 6 units in the x-direction and 4 units in the y-direction, this is similar to saying move 3 units in the x-direction and 2 units in the y-direction, i.e. Gradient $= \dfrac32$

$\begin{pmatrix} 9 \\ 3 \end{pmatrix} = 3 \begin{pmatrix} 3 \\ 1 \end{pmatrix}$
Hence both vectors are parallel, any of them can be used.

If you are still confused, then plot a point on a graph paper, and then use the vector to get another point on the line, you will see that both represent the same direction.

Hope it makes sense.

Your answer to the first part is the same as the one in the book, as the vectors (3,1) and (9,3) point in the same direction. [ (9,3) = 3*(3,1) ]

Just to confirm something say I had the vector equation:
(4, 12) + t(9, 3)

I WOULD be able to cancel down the (9, 3) as it is a direction vector but I WOULD NOT be able to do this to the (4, 12) because it is a position vector...?