I think the issue was that the solution was a vector function

L(t) = r_0 + v_0(t - t_0) (1)

But the students were all using what they knew from a previous section that the equation of a line in space is of the form

L(t) = r_0 + D*(t) (2)

And the problem did not say that the value of t at r_0 needed to be the same for the curve r(t) and the tangent line L(t).

I am wondering if there is a vector function checker out there that would accept (2) as an answer when the formula for the answer is (1)