Which of the following is a necessary condition for two vectors to be equal?

The two vectors must be parallel to each other.
The two vectors must represent the same physical quantity.
The two vectors must have the same magnitude.
The two vectors must not represent the same physical quantities.

Correct answer: The two vectors must represent the same physical quantity.

Solution

For two vectors to be equal, they must have identical magnitude, identical direction, and represent the same physical quantity. All three are necessary; however, representing the same physical quantity is the often-overlooked necessary condition that distinguishes physically equal vectors.

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