Let v = αi + 2j - 3k, w = 2αi + j - k and u be a vector such that |u| = a > 0.

Question

Let \(\vec v = \alpha\hat i + 2\hat j - 3\hat k, \vec w = 2\alpha\hat i + \hat j - \hat k\), and \(\vec u\) be a vector such that \(|\vec u| = \alpha > 0\). If the minimum value of the scalar triple product \([\vec u\;\; \vec v\;\;\vec w]\) is \(-\alpha\sqrt{3401}\) and \(|\vec u.\hat i|^2 = \frac mn\) where m and n are coprime natural numbers, then m + n is equal to ______.

Answer 1

m + n = 3401 + 100 = 3501