Question

Problem 11

Answer 1

Given information

Given 

To determine the vector   , given the vectors   and   in Fig. 3-35.

Step-by-step explanation

Step 1.

To get the difference between vectors  and  ,

resolve the  and  components of each vector

get the difference between the  and  components of the two vectors

use the Pythagorean theorem and the inverse tangent equation to calculate the magnitude and the direction of the resultant vector.

Recall that the  and  components of any given vector  can be calculated as follows.

 

where   is the magnitude of the vector and   is the angle that the vector makes with the  axis.

The magnitude of vector   is   and  is  . Meanwhile, the magnitude of  is  and  is  or  as measured from the  axis.

From these, write the equations for the components of the vectors.

For vector  

 

For vector  ,