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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??????

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??????

Grade:12

1 Answers

vikas askiitian expert
509 Points
10 years ago

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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