The result of scaling the vector $(3, -2)$ by $-2$ yields the new vector $(-6, 4)$.

When scaling a vector, each of its components is multiplied by the scaling factor. In this case, the vector $(3, -2)$ has components $3$ and $-2$, and the scaling factor is $-2$. To determine the new vector, we perform the following calculations: multiply $3$ by $-2$ and $-2$ by $-2$.

For the first component, we calculate:

For the second component, we compute:

Thus, the resulting scaled vector is $(-6, 4)$.

Scaling a vector not only alters its length but also its direction. If the scaling factor is positive, the direction of the vector remains unchanged; however, if the scaling factor is negative, the direction is reversed. In this example, since the scaling factor is $-2$, the vector not only changes in length but also points in the opposite direction. The absolute value of the scaling factor, which is $2$, indicates that the length of the vector is doubled, while the negative sign signifies the reversal of direction.

This concept of vector scaling is particularly valuable in various fields, such as physics and computer graphics, where vectors represent critical quantities like force and velocity. A solid understanding of how to scale vectors effectively enables the manipulation of these quantities in practical applications.