Multiply a Vector by a Scalar

Definition: When a vector is multiplied by a scalar, the size of the vector is “scaled” up or down. Multiplying a vector by a positive scalar will only change its magnitude, not its direction. When a vector is multiplied by a negative scalar, the direction will be reversed.

To multiply a vector by a scalar, multiply each component separately:

c · <a, b> = <c · a, c · b>

Example: Multiply vector a by 2.

Vector a = <1, 4>

Solution:

To multiply vector a by 2, multiply each component by 2:

2 * <1, 4>
= <2*1, 2*4>
= <2, 8>

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