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When are two vectors considered to be equivalent?
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Vectors with the same length and direction, such as those below, are said to be equivalent.

Since we want a vector to be determined solely by its length and direction, equivalent vectors are regarded as the same vector even though they may be in different positions. Equivalent vectors are also said to be equal, which we indicate by writing
$$\mathbf{v}=\mathbf{w}$$

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