Why can't we apply the Parallelogram Rule of vector addition for two parallel vectors? My textbook says that we can't apply the Parallelogram Rule of vector addition for two parallel vectors. Why can't we apply the rule?
 A: Because you cannot build a proper parallelogram from two collinear segments.
A: If you call a Parallelogram with angles 0 a parallelogram , you still can use it, but most people just ad two parallel vectors as in  one line.
A: The parallelogram vector addition says that if two vectors have the same point as its tail or origin then consider them as two adjacent sides of a parallelogram and construct a parallelogram. And then the diagonal of that parallelogram (through the tail of those vectors ) will give you the direction of the resultant vector and for magnitude, you know the rules.
If you are given two parallel vectors, it is quite sure and obvious that you can't consider them as the adjacent sides of a parallelogram and hence tey get overlapped and you are left with just one vector whose magnitude is the algebraically added magnitude of the two vectors and pointing in the same direction.

You can't make a parallelogram (I am not talking about a degenerate parallelogram ) by taking two parallel sides as the adjacent sides since in that case, they would no longer be parallel to each other.
Hope it helps ☺️.
A: If you call the degenerate parallelogram where all four vertices a colinear, and the four interior angles are 0, 180, 0 and 180 degrees, still a "parallelogram", then you can use the parallelogram rule for parallel (and antiparallel) vectors. Similarly, if you allow a side of a parallelogram to have length zero, then you can use the parallelogram rule if one or both of the vectors are the zero vector.
Jeppe Stig Nielsen's comment posted as answer
