c^{2}
a^{2}
b^{2} or c
a^{2}
b^{2}
Vectors
ANALYTICAL METHOD OF VECTOR ADDITION
Rev. 0
Page 23
CP02
Figure 22 Right Triangle
ANALYTICAL METHOD OF VECTOR ADDITION
Vector components are added to determine the magnitude and direction of the
resultant. Calculations using trigonometric functions are the most accurate
method for making this determination.
EO 1.3
ADD vectors using the following methods:
c.
Analytical
The graphic and components addition methods of obtaining the resultant of several vectors
described in the previous chapters can be hard to use and time consuming. In addition, accuracy
is a function of the scale used in making the diagram and how carefully the vectors are drawn. The
analytical method can be simpler and far more accurate than these previous methods.
Review of Mathematical Functions
In earlier mathematics lessons, the Pythagorean Theorem was used to relate the lengths of the
sides of right triangles such as in Figure 22. The Pythagorean Theorem states that in any right
triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths
of the other two sides. This expression may be written as given in Equation 24.
(24)

