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NDA2014MathematicsThree Dimensional GeometryActual

Paragraph : The vertices of a triangle A B C are A(2,3,1), B(-2,2,0) and C(0,1,-1) . Question : What is the cosine of angle ABC ?

Options

  1. A1 3
  2. B1 2
  3. C2 6
  4. DNone of the above

Correct answer

A. 1 3

Step-by-step solution

aligned & a= BC = (2)^2+(-1)^2+(-1)^2 = 4+1+1 = 6 & b= CA = (2)^2+(2)^2+(2)^2 = 4+4+4 = 12 & c= AB = (4)^2+(1)^2+(1)^2 = 16+1+1 = 18 . aligned aligned B & = a^2+c^2-b^2 2 a c = 6+18-12 2 6 18 & = 12 2 108 = 12 2 6 3 = 1 3 aligned

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