Q24E - University Physics with Modern Physics

Question

For the vectors  $\overline{A}$ and $\overrightarrow{B}$ in Fig. E1.24, use a scale drawing to find the magnitude and direction of (a) the vector sum  $\overline{A}$+ $\overrightarrow{B}$ and (b) the vector difference.  $\overline{A}$- $\overrightarrow{B}$ Use your answers to find the magnitude and direction of (c) -$\overline{A}$- $\overrightarrow{B}$ and (d) $\overrightarrow{B}$- $\overline{A}$(See alsoExercise 1.31 for a different approach.)

                                       

Step-by-Step Solution

Answer

The value of $A+B$ is $9 m$, the value of $A- B$ is $22 m$, the value of $–A-B$ is also $22$ but different direction and $B-A$ is $9$ meter.

Step 1: Determining the length

Calculate the length of the 15.0-meter vector and use it as $\mathrm{x}$. Then, for sections (a) and (b), measure the length Here,

To calculate the appropriate distances and angles, use a ruler and a protractor, accordingly. if the vector sums and enter that value in for z. To find the magnitude, solve for y. To determine any angles, use a protractor.

$\frac{15}{x}=\frac{y}{z}$

The above equation can be used in drawing the further figure.

Step 2 : Calculation of the vector sum A → + B →

Draw the parallelogram that  $\overline{A}$ and  $\overrightarrow{B}$ create. The vector from the origin to the opposite corner of the parallelogram is their sum.

                                   

                                                          A+ B vector diagram 

Step 3: For calculation of part B A - B

The vector B has the same magnitude and direction as  $-B$  but points in the opposite sense. Draw the parallelogram formed by  $A$  and  $-B$  and the vector from the origin to the opposite corner of the parallelogram. This is the sum $A - B$.

Step 4: For calculation of part B - ( A + B )

$-(A -B = -( A + B)$ has the same magnitude and direction as $A+ B$ but opposite sense.

                                          

                                                               Ray diagram for case 3 

Step 5:For calculation of part D B - A

$B-A$have same value as $A- B$ but only direction will be changed for option D is similar to that of B.

                                             

                                     

                                                    Diagram for case for

Hence here the value of $A+B$is $9 m$, the value of$A- B$ is $22 m$, the value of$–A-B$ is also $22$ but different direction and $B-A$ is $9$ meter