Answer
The point represent as $(4,3,6)$ .
Work Step by Step
Given that the direction indices for a vector that passes from point
$\frac{1}{3},\frac{1}{2},0$ to the point $\frac{2}{3},\frac{3}{4},\frac{1}{2}$
So the point is represented as
$x_{1}=\frac{a}{3}$
$y_{1}=\frac{b}{2}$
$z_{1}=0c=0$
Similarly the point 2 is represented as
$x_{2}=\frac{2a}{3}$
$y_{2}=\frac{3b}{4}$
$z_{2}=\frac{c}{2}$
Equation representation of u,v and w
$u=n(\frac{x_{2}-x_{1}}{a})$
$v=n(\frac{y_{2}-y_{1}}{b})$
$z=n(\frac{z_{2}-z_{1}}{c})$
Denominator in the fraction has highest value of 3 and 4. So the value of n =12
$u=12(\frac{\frac{2a}{3}-\frac{a}{3}}{a})=4$
$v=12(\frac{\frac{3b}{4}-\frac{b}{2}}{b})=3$
$z=12(\frac{\frac{c}{2}-0}{c})=6$
The point is represented as $(4,3,6)$ .
