Q43E - University Physics with Modern Physics

Question

 For the vectors $\overrightarrow{A}$,$\overrightarrow{B}$ and $\overrightarrow{C}$ in Fig. E1.24, find the scalar

products . (a) $\overrightarrow{A}.\overrightarrow{B}$; (b) $\overrightarrow{B}.\overrightarrow{C}$; (c) $\overrightarrow{A}.\overrightarrow{C}$

Step-by-Step Solution

Answer

The scalar product of  $\overrightarrow{A}.\overrightarrow{B}$, $\overrightarrow{B}.\overrightarrow{C}$, and $\overrightarrow{A}.\overrightarrow{C}$ are and $-100m^{2 },150m^2,71m^2$.

 

Given Data

$$\begin{gathered} \overrightarrow{A}=\left(8.00m\right) \\ \overrightarrow{B}=\left(15.0m\right) \\ \overrightarrow{C}=\left(12.0m\right) \end{gathered}$$

The scalar product of A → . B →

The angle of $\overrightarrow{A}.\overrightarrow{B}$,$150°$

              =$AB\cos \theta$ 

                         =$\left(8\times 15\right)\cos 150$

                         =$83.91\approx -100m^2$

The scalar product of B → . C →

The angle of  $\overrightarrow{B}.\overrightarrow{C}$, $145°$

= $BC\cos \theta$

            = $\left(15\times 12\right)\cos 145$

            = $159.09\approx 150m^2$

The scalar product of

  The angle of  $$ ,${65}^{°}$

=$AC\cos \theta$
            =$\left(8\times 12\right)\cos 65$

             = $-53.99\approx 71m^2$