Answer
$(\dfrac{5}{2},1,6)$
Work Step by Step
Formula to calculate the unit vector $\hat{\textbf{u}}$ is: $\hat{\textbf{u}}=\dfrac{u}{|u|}$
Since, $u=\overrightarrow{P_1P_2}=P_2-P_1$
Here,$P_1$ and $P_2$ are two vectors.
or, $u=(4-1)i+(-2-4)j+(7-5)k=3i-6j+2k$; $|u|=\sqrt{(3)^2+(-6)^2+(2)^2}=\sqrt {49}=7$
Thus, $\hat{\textbf{u}}=\dfrac{3i-6j+2k}{7}=(\dfrac{3}{7} i-\dfrac{6}{7}j+\dfrac{2}{7}k)$
Apply Mid-point formula.
Thus, we have $(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2},\dfrac{z_1+z_2}{2})=(\dfrac{1+4}{2},\dfrac{4+(-2)}{2},\dfrac{5+7}{2})$
or, $=(\dfrac{5}{2},1,6)$
