Answer
The components of the vector ${\bf{v}}$:
${\bf{v}} = \left( {0,\frac{1}{2}, - \frac{1}{2}} \right)$
Work Step by Step
From Figure 18 we have $A = \left( {1,0,1} \right)$, $B = \left( {1,1,0} \right)$ and $C = \left( {0,1,1} \right)$.
Since the midpoint of $\left( {{a_1},{a_2},{a_3}} \right)$ and $\left( {{b_1},{b_2},{b_3}} \right)$ is given by $\left( {\frac{{{a_1} + {b_1}}}{2},\frac{{{a_2} + {b_2}}}{2},\frac{{{a_3} + {b_3}}}{2}} \right)$, so
1. the midpoint of segment $\overline {AC} $ is $\left( {\frac{{0 + 1}}{2},\frac{{1 + 0}}{2},\frac{{1 + 1}}{2}} \right) = \left( {\frac{1}{2},\frac{1}{2},1} \right)$
2. the midpoint of segment $\overline {BC} $ is $\left( {\frac{{0 + 1}}{2},\frac{{1 + 1}}{2},\frac{{1 + 0}}{2}} \right) = \left( {\frac{1}{2},1,\frac{1}{2}} \right)$
Let ${\bf{v}}$ be the vector whose tail and head are the midpoints of segments $\overline {AC} $ and $\overline {BC} $. So, ${\bf{v}}$ is based at $\left( {\frac{1}{2},\frac{1}{2},1} \right)$ and its head is at $\left( {\frac{1}{2},1,\frac{1}{2}} \right)$. Thus, the components of ${\bf{v}}$ are
${\bf{v}} = \left( {\frac{1}{2},1,\frac{1}{2}} \right) - \left( {\frac{1}{2},\frac{1}{2},1} \right) = \left( {0,\frac{1}{2}, - \frac{1}{2}} \right)$.
