You can find a [b]unit[b] vector (norm= 1) parallel to a given vector by dividing by the norm. Multiplying a given vector by any number will give a parallel vector. Yes, two vectors are perpendicular if and only if their dot product is 0.
Okay: find a unit vector parallel to the vector 2i+ 3j- 4k. Find a vector parallel to 2i+ 3j- 4k that has length twice as long!
Relatively easy problem, find a vector, in the xy-plane, perpendicular to 3i+ 4j. Slightly harder, find a vector perpendicular to 4i- 3j+ 2k.