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Beginning Math and Physics for Game Programmers by Wendy Stahler

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Scalar Multiplication

I'm sure for many years you have been multiplying scalars by other scalars. Remember, a scalar quantity is just an ordinary number. Let's turn our attention to a scalar times a vector. If you think about a vector expressed in polar coordinates, all you have is a magnitude and a direction. When you multiply a scalar by that vector, all you're really doing is changing the magnitude by scaling it up or down. If the scalar value is a whole number, the magnitude gets larger. Likewise, if the scalar is a fraction less than 1, the magnitude gets smaller.

Scalar Multiplication in Polar Coordinates

for any scalar c and vector .

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