imo class 12 vector algebra

Which of the following is a unit vector parallel to the vector a = 2î − ĵ + 2k̂?

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Which of the following is a unit vector parallel to the vector a = 2î − ĵ + 2k̂?

  • A. (2î − ĵ + 2k̂)/3
  • B. (2î − ĵ + 2k̂)/4
  • C. (î − ĵ + k̂)/√3
  • D. (2î + ĵ − 2k̂)/3

Answer: A) (2î − ĵ + 2k̂)/3

Explanation: Magnitude of a = √(2² + (−1)² + 2²) = √9 = 3. Unit vector = a / |a| = (2î − ĵ + 2k̂)/3.

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