question_answer

Let \[\sqrt{3}\hat{i}+\hat{j},\,\,\hat{i}+\sqrt{3}\hat{j}\] and \[\beta \hat{i}+(1-\beta )\hat{j}\] respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle between OA and OB is \[\frac{3}{\sqrt{2}},\] then the sum of all possible values of \[\beta \] is

Answer:

1