Can sum of two equal vectors be equal to either of the vectors

General
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can sum of two equal vectors be equal to either of the vectors

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Can the sum of two equal vectors be equal to either of the vectors?

Answer: No, the sum of two equal vectors cannot be equal to either of the vectors themselves. Here’s why:

  1. Understanding Vectors:

    • A vector has both magnitude and direction. When adding vectors, you must take both into account.

  2. Vector Addition:

    • When two vectors are added, their magnitudes are combined according to both their magnitude and direction. If the vectors are equal, they can be represented as \vec{A} and \vec{A}.

  3. Sum of Equal Vectors:

    • Using vector addition, the sum of two equal vectors \vec{A} + \vec{A} is:

      2\vec{A}

    • This result is a new vector with the same direction as \vec{A} but twice its magnitude.

  4. Conclusion:

    • Since 2\vec{A} has a greater magnitude than either of the original vectors \vec{A}, the sum cannot be equal to either \vec{A}.

Summary: The sum of two identical vectors results in a vector with double the magnitude of one vector, so it cannot equal either of the original vectors.