Scalar Multiplication of a Vector

We've discussed vector addition and subtraction. Now, we'll explore scalar multiplication, an operation that combines a vector and a scalar (a regular number).

Recall that multiplication of scalars can be interpreted as repeated addition. For example, $4 \times 3 = 4 + 4 + 4$ . We use a similar idea to define scalar multiplication of a vector. If we have a vector $\overrightarrow{X}$ , then $3 \times \overrightarrow{X}$ (written as $3\overrightarrow{X}$ ) is defined as:

$3\overrightarrow{X} = \overrightarrow{X} + \overrightarrow{X} + \overrightarrow{X}$

This operation is called scalar multiplication because we are multiplying a vector by a scalar.

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