Page 17 - mechanics

Chapter – 3 Concurrent forces in 3D

Thus, a position vector between two points in space is
obtained by subtracting the coordinates of the starting point
from the corresponding ones of the end point. A statement that
exactly represents the position vector formation in 2D.

3.3 Unit Vector

In this section we list three possible situations to obtain a
unit vector:

Case 1: if the vector is given in its Cartesian form, then

uA = A = Ax i + Ay j + Az k (3.11)

AA A A

Case 2: if the coordinate angles of the vector are given, from

equation (3.7)

uA = cos i + cos  j+ cos k (3.12)

Case 3: if the coordinates of two points A and B on the vector
are known, then

ur = (x B − x A )i + (y B − y A )j+ (z B − z A )k (3.13)
(x B − x A )2 + (y B − y A )2 + (z B − z A )2

From the equation (3.12) and the fact that the magnitude of a
unit vector equals one, then

cos2  + cos2  + cos2  =1 (3.14)

83