A Classical Approach of Newtonian Mechanics

3 MOTION IN 3 DIMENSIONS 3.4 Vector addition

R

O

Figure 12: Vector addition

z-axes), finally move z meters along the z-axis (perpendicular to both the x- and

y-axes). Note that a positive x value is interpreted as an instruction to move x

meters along the x-axis in the direction of increasing x, whereas a negative x value

is interpreted as an instruction to move |x| meters along the x-axis in the opposite
direction, and so on.

1.17 Vector addition

Suppose that the vector displacement r of some point R from the origin O is
specified as follows:

r = r 1 + r 2. (3.2)

Figure 12 illustrates how this expression is interpreted diagrammatically: in order

to get from point O to point R, we first move from point O to point S along vector

r 1 , and we then move from point S to point R along vector r 2. The net result is the

same as if we had moved from point O directly to point R along vector r. Vector
r is termed the resultant of adding vectors r 1 and r 2.

Note that we have two ways of specifying the vector displacement of point
S from the origin: we can either write r 1 or r − r 2. The expression r − r 2 is

interpreted as follows: starting at the origin, move along vector r in the direction

of the arrow, then move along vector r 2 in the opposite direction to the arrow.

In other words, a minus sign in front of a vector indicates that we should move

along that vector in the opposite direction to its arrow.

S

r 2

r 1

r