If '0.8 i + 0.5 j + ck' represents a unit vector, the value of 'c' is:
Correct answer: E. √0.11
- A. √0.64
- B. √0.66
- C. 1
- D. 0.2
- E. √0.11
Explanation
The magnitude of the given vector is:|0.8i + 0.5j + ck| = √(0.8² + 0.5² + c²)For the given vector to be a unit vector, its magnitude must be 1. So,√(0.8² + 0.5² + c²) = 10.64 + 0.25 + c² = 1c² = 1 - 0.64 - 0.25 = 0.11c= √0.11Therefore, the value of c is √0.11 or approximately 0.33. Hence, the correct answer is E.
This question appeared on the NUMS 2019 (cancelled sitting) paper, which you can sit online with every answer explained.
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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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