imo class 12 vector algebra

The position vectors of the vertices A, B, C of a triangle are î + ĵ, ĵ + k̂, and k̂ + î respectively. What is the position vector of its centroid?

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The position vectors of the vertices A, B, C of a triangle are î + ĵ, ĵ + k̂, and k̂ + î respectively. What is the position vector of its centroid?

  • A. (2î + 2ĵ + 2k̂)/3
  • B. (î + ĵ + k̂)/3
  • C. 2î + 2ĵ + 2k̂
  • D. î + ĵ + k̂

Answer: A) (2î + 2ĵ + 2k̂)/3

Explanation: Centroid = (a + b + c)/3 = (î + ĵ + ĵ + k̂ + k̂ + î)/3 = (2î + 2ĵ + 2k̂)/3.

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