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Scalar multiplication

The next operation we can perform with vectors will make clear why we call a scalar a scalar. If we want to make a vector bigger of smaller, all we do is scale it by multiplying the whole vector by a single number, a scalar. If this scalar is bigger than one, the new vector will point in exactly the same direction as the old, but will be longer. If the scalar is between zero and one, the new vector will not change direction, but will shrink to be smaller than the original vector. Multiplying a vector by a negative scalar has two effects. The first is to make the vector longer or shorter. The second effect is to turn the vector around and make it point in the opposite direction.



Vector Calculus
Mon Jul 14 10:10:30 MST 1997