Find the Cartesian equation of the line passing through $(3,-2,-5)$ and $(3,-2,6)$ in $3$D.
The equation of the line through the points $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ is given by $$ \vec{r}=\vec{a}+\lambda(\vec{b}-\vec{a}) $$ where $\vec{a}=x_1\hat{i}+y_1\hat{j}+z_1\hat{k}$ and $\vec{b}-\vec{a}=(x_2-x_1)\hat{i}+(y_2-y_1)\hat{j}+(z_2-z_1)\hat{k}$ $$ \frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1} $$
For the line through the points $(3,-2,-5)$ and $(3,-2,6)$ is $$\lambda= \boxed{\frac{x-3}{0}=\frac{y+2}{0}=\frac{z+5}{11}} $$
Is it the correct solution and how do I make sense of the final equation of the line through the given points ?
the
equation… $\endgroup$ – Bernard Jul 29 '18 at 9:30