3.9 - Multiplying polar vectors by a scalar
Multiplying a vector represented in polar notation by a positive scalar requires only one
multiplication operation: Multiply the magnitude of the vector by the scalar. The angle is
unchanged.
Let’s say there is a vector of magnitude 50 km with an angle of 30°. You are asked to
multiply it by positive three. This situation is shown in Example 1 to the right. Since you
are multiplying by a positive scalar, the angle stays the same at 30°, and so the answer
is 150 km at 30°.
If you multiply a vector by a negative scalar, multiply its magnitude by the absolute
value of the scalar (that is, ignore the negative sign). Then change the direction of the
vector by 180° so that it points in the opposite direction. In polar notation, since the
magnitude is always positive, you add 180° to the vector's angle to take its opposite.
The result of multiplying (50 km, 30°) by negative three is (150 km, 210 °).
If adding 180° would result in an angle greater than 360°, then subtract 180° instead.
For instance, in reversing an angle of 300°, subtract 180° and express the result as
120° rather than 480°. The two results are identical, but 120° is easier to understand.
Multiplying polar vector by
positive scalar
Multiply vector's magnitude by scalar
Angle unchangedMultiplying by negative scalar
Use absolute value and reverse
direction