3

Vectors

Vector Addition Versus Scalar Addition

Keep in mind that A + B = C is very different from A + B = C. The first is a vector sum, which must be handled carefully, such as with the graphical method described here. The second is a simple algebraic addition of numbers that is handled with the normal rules of arithmetic.

Component Vectors Versus Components

The vectors A_x and A_y are the component vectors of A. These should not be confused with the scalars A_x and A_y, which we shall always refer to as the components of A.

x and y Components

Equations 3.8 and 3.9 associate the cosine of the angle with the x component and the sine of the angle with the y component. This is true only because we measured the angle with respect to the x axis, so don't memorize these equations. If is measured with respect to the y axis (as in some problems), these equations will be incorrect. Think about what side of the triangle containing the components is adjacent to the angle and what side is opposite, and assign the cosine and sine accordingly.

Tangents on Calculators

Generally, the inverse tangent function on calculators provides an angle between - 90° and +90°. As a consequence, if the vector you are studying lies in the second or third quadrant, the angle measured from the positive x axis will be the angle your calculator returns plus 180°.