Hi

Note that for the first question not only t=2 but also t=-1 give perpendicular vectors. There is no possibility to get parallel vectors.

For the second question see the sketch where u = 3i + 2j - 6k and d = 2i - 4j + k

You can see that the dot product of u and d is :

u.d = (td).d = t (d.d)

Therefore t = d.d / u.d