Which one is a unit vector ?
Correct answer: D. Both B and C are correct
- A. ??3 i^ + ??3 j^ + ??3 k^
- B. 1/??3 i^ + 1/??3 j^ +1/ ??3 k^
- C. ??3 / 3 i^ + ??3 / 3 j^ + ??3 / 3 k^
- D. Both B and C are correct
Explanation
Assuming the damaged symbols represent square roots, the vector in b has magnitude √[(1/√3)² + (1/√3)² + (1/√3)²] = √(3 x 1/3) = 1, so it is a unit vector. Since √3/3 = 1/√3, option c represents exactly the same vector, making d correct. Students may choose only b because they do not recognise that 1/√3 and √3/3 are equal.
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About Addition of Vectors
Vector addition combines directed quantities using the head-to-tail, parallelogram and component methods. Work includes finding the resultant magnitude and direction for two or more vectors, resolving vectors into perpendicular components, and distinguishing vector addition from scalar addition, where direction has no role.
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