Question

Find the vector and cartesian equation of the line that passes through the points $(3-2-5)$ and $(3-26)$

Answer 1

Vector equation $\overrightarrow{r}=\overrightarrow{a}+\lambda (\overrightarrow{b}-\overrightarrow{a})$

$=(3\hat{i}-2\hat{j}-5\hat{k})+\lambda ((3-3)\hat{i}+(-2+2)\hat{j}+(6-5)\hat{k})$

$=(3\hat{i}-2\hat{j}-5\hat{k})+\lambda \left(11\hat{k}\right)$
Cartesian equation of the line $\frac{x-3}{0}=\frac{y+2}{0}=\frac{z+5}{11}$