if a and b are real nos between 0 and 1 such tht the points (a,1) , (1,b) and(0,0) form an equilateral triangle thn find a and b??????

A,B,C are the vertices of triangle ...

A , B , C are (00) , (a,1) ,(1,b) respectively

vector AB =  (ai + j)  ,vector AC = (i + bj) & vector BC = ((1-a)i + (b-1)j)

now since the triangle is equilateral so

 magnitude of AB,BC,AC is equal

so , a² + 1 = b² +1 ........1

   a²+1 = (1-a)² + (b-1)² ...........2

solving these

  a=b =(2-sqrt3)