Chapter 8.3, Problem 35E

To determine

To prove: the given condition.

Answer to Problem 35E

See explanation

Explanation of Solution

Given information:

  $\left|\overrightarrow{G_1{G}_2}\right|=\left|\overrightarrow{G_2{G}_1}\right|$

Calculation:

Let $\overrightarrow{G_1}\text{ and }\overrightarrow{G_2}$ as follows:

  $\begin{array}{l}\overrightarrow{G_1}=\langle x_1,y_1,z_1\rangle \\ \overrightarrow{G_2}=\langle x_2,y_2,z_2\rangle \end{array}$

Simplify $\left|\overrightarrow{G_1{G}_2}\right|$ as shown below.

  $\begin{array}{c}\left|\overrightarrow{G_1{G}_2}\right|=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2+{\left(z_2-z_1\right)}^2}\\ =\sqrt{{\left(x_1-x_2\right)}^2+{\left(y_1-y_2\right)}^2+{\left(z_1-z_2\right)}^2}\\ =\left|\overrightarrow{G_2{G}_1}\right|\end{array}$

Thus, the given condition is proved.