Chapter 8.3, Problem 38E

To determine

To find: the midpoint of $\overrightarrow{\text{v}}$ .

Answer to Problem 38E

  $\langle 3,4,4\rangle$

Explanation of Solution

Given information:

The vector $\overrightarrow{\text{v}}$ extends from $V\left(2,3,6\right)$ to $W\left(4,5,2\right)$ .

Calculation:

Let the midpoint of a vector $\overrightarrow{\text{v}}$ be $M$ .

The midpoint of a vector $\overrightarrow{\text{v}}$ is same as the midpoint of a line segment

  $\overline{VW}$ which can be evaluated as follows:

  $\begin{array}{c}M=\frac{1}{2}\langle \left(x_V+x_W\right),\left(y_V+y_W\right),\left(z_V,z_W\right)\rangle \\ =\frac{1}{2}\langle 2+4,3+5,6+2\rangle \left[\text{Put the point coordinates}\right]\\ =\frac{1}{2}\langle 6,8,8\rangle \\ =\langle 3,4,4\rangle \end{array}$

Thus, the midpoint of given vector is $\langle 3,4,4\rangle$ .