https://boredofstudies.org/threads/vector-projections-qs-help-plz-ugrent.394192/

The third question sounds simple but I believe it has been set in error as there is no simple solution. The posts in the thread do explore some aspects of the problem and could be adapted to a problem in proof.

Perhaps as something like:

If is the origin, is a variable point satisfying , and is a triangle of area 10 u

^{2}, show that can be located anywhere on the number plane so long as , and find the value of .