I was attempting a question on vector algebra.
If $a,b,c$ are unit vectors satisfying :
$|a-b|^2 +|b-c|^2 +|c-a|^2 =9$, find the value of $|2a + 5b + 5c|.$
This was the solution:
($a\cdot b+b\cdot c+c\cdot a=-3/2,$ they directly assumed all $3$ angles to be $120$ degrees)
This assumption baffled me. Yet it gave them the correct answer.
When are such assumptions valid, or, when can such an assumption give us a correct answer and when will it fail?