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AP EAMCET2013MathematicsVector Algebra

The points whose position vectors are 2 i +3 j +4 k , 3 i +4 j +2 k and 4 i +2 j +3 k are the vertices of

Options

  1. Aan isosceles triangle
  2. Bright angled triangle
  3. Cequilateral triangle
  4. Dright angled isosceles triangle

Correct answer

C. equilateral triangle

Step-by-step solution

aligned & Let a =2 i +3 j +4 k = OA & b =3 i +4 j +2 k = OB & and c =4 i +2 j +3 k = OC & A B=O B-O A=i+j-2 k & B C=O C-O B= i -2 j + k & and C A=O A-O C=-2 i+j+k & Now, A B= 1+1+4 = 6 & BC = 1+4+1 = 6 & and CA = 4+1+1 = 6 & aligned Since, the length of all three sides are equal. So, the triangle is an equilateral triangle.

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