Vector BA÷ the modulus of vector BA represents the unit vector with the direction in vector BA. Therefore, the modulus vector BA of the vector BA+ the modulus vector BC of the vector BC refers to the vector in the direction of the bisector of the angle ABC. The second condition shows that the bisector of angle ABC is perpendicular to AC, so there is AB=BC. From the first condition, we can know that √3a=2bsinA, and change the edge into an angle from sine theorem, that is √3sinA=2sinBsinA, because Sina >；; 0, so sinB=√3/2, thus obtaining B=60 degrees (it has been explained that b is an acute angle, and if it is not an acute angle, it may be an isosceles obtuse triangle), so it is an equilateral triangle.