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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)
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)
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