How are the two vectors of the same magnitude oriented to get a resultant of the same magnitude?
Correct answer: D. 120°
- A. 90°
- B. 60°
- C. 45°
- D. 120°
Explanation
120°: If two vectors of the same magnitude are oriented at 120 degrees to each other, the resultant vector will have a magnitude that is greater than the individual vectors. The magnitude of the resultant vector can be calculated using the law of cosines: magnitude of resultant = sqrt(magnitude of individual vector^2 + magnitude of individual vector^2 - 2 * magnitude of individual vector * magnitude of individual vector * cos(θ)) Where θ is the angle between the vectors. In this case, since θ is 120 degrees, the resultant vector will have a magnitude that is greater than the magnitude of each individual vector.
This question appeared on the ETEA MDCAT 2009 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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