Basic Technical Mathematics, 11th Edition

9.3 Vector Addition by Components

• Adding Vectors at Right Angles • Adding Vectors by Components

Now that we have developed the meaning of the components of a vector, we are able to add vectors to any degree of required accuracy. To do this, we use the components of the vector, the Pythagorean theorem, and the tangent of the standard-position angle of the resultant. In the following example, two vectors at right angles are added.

EXAMPLE 1 Adding vectors at right angles

Add vectors A and B, with $A\hspace{0.17em}=\hspace{0.17em}14.5$ and $B\hspace{0.17em}=\hspace{0.17em}\mathrm{9.10.}$ The vectors are at right angles, as shown in Fig. 9.21.

Fig. 9.21

We can find the magnitude R of the resultant vector