# Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, - 1, 1), Q(1/2, 1/3, 1/4)

Find the vector and parametric equations for the line segment connecting P to Q.
P(0, - 1, 1), Q(1/2, 1/3, 1/4)

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Szeteib
Vector equation of a line segment joining the points with position vectors ${r}_{0}$ and ${r}_{1}$ is
$r=\left(1-t\right){r}_{0}+t{r}_{1}$
Where $t\in \left[0,1\right]$
Substitute ${r}_{0}=<0,-1,1>$ and ${r}_{1}=<\frac{1}{2}.\frac{1}{3},\frac{1}{4}>$
$r\left(t\right)=\left(1-t\right)\left(0,-1,1\right)+t<\frac{1}{2},\frac{1}{3},\frac{1}{4}>$
$r\left(t\right)=<0,-1+t,1-t>+<\frac{t}{2},\frac{t}{3},\frac{t}{4}>$
$r\left(t\right)=<\frac{t}{2},-1+\frac{4t}{3},1-\frac{3t}{4}>$
Where $t\in \left[0,1\right]$ The parametric equations for the line segment are
$x=\frac{t}{2},y=-1+\frac{4t}{3},z=1-\frac{3t}{4}$
Where $t\in \left[0,1\right]$