1. ## Vector Midpoint Problem

What is the vector whose tail and head are the midpoint of and the midpoint of , respectively.

2. The midpoint of $\displaystyle AB$ is $\displaystyle \displaystyle M\left(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2},\frac{z _A+z_B}{2}\right)$
So $\displaystyle \displaystyle M\left(0,7,\frac{5}{2}\right)$
The midpoint of $\displaystyle BC$ is $\displaystyle \displaystyle N\left(\frac{15}{2},\frac{15}{2},\frac{9}{2}\right )$
Then the vector is
$\displaystyle \displaystyle \overrightarrow{MN}=\left(x_N-x_M\right)\overrightarrow{i}+\left(y_N-y_M\right)\overrightarrow{j}+\left(z_N-z_M\right)\overrightarrow{k}=\frac{15}{2}\overrigh tarrow{i}+\frac{1}{2}\overrightarrow{j}+2\overrigh tarrow{k}$

3. Originally Posted by Del

What is the vector whose tail and head are the midpoint of and the midpoint of , respectively.

1. Use the midpoint formula to calculate the coordinates of head and teil of the vector $\displaystyle \vec v$

$\displaystyle M_{AB}\left(\frac{-5+5}2\ ,\ \frac{6+8}2\ ,\ \frac{4+1}2 \right)~\implies~ M_{AB}\left(0\ ,\ 7\ ,\ \frac{5}2 \right)$

$\displaystyle M_{BC}\left(\frac{15}2\ ,\ \frac{15}2\ ,\ \frac{9}2 \right)$

$\displaystyle \vec v=\overrightarrow{M_{AB} M_{BC}} = \overrightarrow{OM_{BC}} - \overrightarrow{OM_{AB}} = \left(\frac{15}2\ ,\ \frac{1}2\ ,\ 2\right)$