Answer
$\left( 1, \frac{14}{3}, -\frac{5}{3}\right)$
Work Step by Step
Step 1.
Calculate the distance between points $P_1( 1, 4, -3)$ and $P_2(1, 5, -1)$:
$d= \sqrt {(x_2 - x_1)^{2} + (y_2 -y_1)^{2} + (z_2 - z_1)^{2}} $
Put $P_1$ and $P_2$ in the above formula:
$P_1P_2=\sqrt {(1-1)^{2} + (5-4)^{2} + (-1 -(-3))^{2}}= \sqrt 5$
Step 2.
Now apply the parametric equation of line
$P= P_1 + u(P_2 - P_1) $ where $u= 2/3$.
$P = <1, 4, -3> + 2/3<0, 1, 2>$
$P = < 1, 4 ,-3 > + <0, 2/3, 4/3>$ i.e. multiplied point $2/3$ into $<0, 1, 2>$.
$P = < 1, 14/3 ,-5/3>$
