the sum of two vectors can be described as the diagonal in a parallelogram with the vectors as its sides. The difference of two vectors gives the second diagonal in this parallelogram.
If then you are dealing with a rhombus and the diagonals are perpendicular that means you are dealing with a right triangle. (See attachment)
The angle between the vectors is . the ratio of the length of the diaogonals is 1 : 100. Thus
. That means:
Now you can calculate the angle between the vectors. I've got: