Let \(\sqrt 3 \hat i + {\rm{\hat j}},{\rm{\hat i}} + \sqrt 3 {\rm{\hat j}},{\rm{\;and\;\beta \hat i}} + \left( {1 - \beta } \right){\rm{\hat j}}\) 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 β is:

Let \(\sqrt 3 \hat i + {\rm{\hat j}},{\rm{\hat i}} + \sqrt 3 {\rm{\hat

1.	Let \(\sqrt 3 \hat i + {\rm{\hat j}},{\rm{\hat i}} + \sqrt 3 {\rm{\hat j}},{\rm{\;and\;\beta \hat i}} + \left( {1 - \beta } \right){\rm{\hat j}}\) 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 β is:
A.	4
B.	3
C.	2
D.	1
Answer» E.