Mice A and B each went on a quest to find food. Their displacements by the end are represented by vectors vec(a) and vec(b), respectively. Which option best describes the meaning of the following statement? || vec(a)||=|| vec(b)∣ Choose 1 answer: (A) The mice finished at the same distance from their starting points, but not necessarily in the same direction. (B) The mice finished at the same distance and in the same direction from their starting points. (C) The mice walked the exact same path.

Question

Mice A and B each went on a quest to find food. Their displacements by the end are represented by vectors vec(a) and vec(b), respectively. Which option best describes the meaning of the following statement?  || vec(a)||=|| vec(b)∣ Choose 1 answer: (A) The mice finished at the same distance from their starting points, but not necessarily in the same direction. (B) The mice finished at the same distance and in the same direction from their starting points. (C) The mice walked the exact same path.

Bytelearn · Accepted Answer

Magnitude of a vector: The magnitude of a vector represents the distance from the starting point to the end point, without considering direction.Equal magnitudes of displacements: Since || vec(a)||=|| vec(b)||, it means the magnitudes of the displacements of mice A and B are equal.Implication of equal magnitudes: This equality in magnitudes implies that both mice ended up the same distance from their starting points.Lack of information on direction: However, the statement does not provide any information about the direction of their displacements.Correct answer explanation: Therefore, the correct answer is (A) The mice finished at the same distance from their starting points, but not necessarily in the same direction.

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