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AP EAMCET201923 Apr 2019Morning ShiftMathematicsVector AlgebraActual

If ( , , ) are distinct real numbers and ( + + 0 ), then the points with position vectors ( i + j + k , i + j + k ) and ( i + j + k ) are

Options

  1. Acollinear
  2. Bvertices of a scalene triangle
  3. Cvertices of an isosceles triangle
  4. Dvertices of an equilateral triangle

Correct answer

D. vertices of an equilateral triangle

Step-by-step solution

Let position vectors are ( aligned & O A = i + j + k & O B = i + j + k , and & O C = i + j + k aligned ) So, ( A B =( - ) i +( - ) j +( - ) k ) ( B C =( - ) i +( - ) j +( - ) k ) and ( C A =( - ) i +( - ) j +( - ) k ) ( | A B |= ( - )^2+( - )^2+( - )^2 ) (| B C |= ( - )^2+( - )^2+( - )^2 ) and (| C A |= ( - )^2+( - )^2+( - )^2 ) ( aligned | A B | & =| B Q |=| C A | & = ( - )^2+( - )^2+( - )^2 0 & [ , , are distinct real numbers ] aligned ) So, given position vectors are vertices of an equilateral triangle. Hence, o

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