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Scalar Multiplication

By Andrew Zimmerman Jones, About.com

Image by Benjamin Esham, available through Wikimedia Commons.

The simplest operation that can be performed on a vector is to multiply it by a scalar. This scalar multiplication alters the magnitude of the vector. In other word, it makes the vector longer or shorter.

When multiplying times a negative scalar, the resulting vector will point in the opposite direction.

Examples of scalar multiplication by 2 and -1 can be seen in the diagram to the right.

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