Question

Find the costesion and vector equation of a line which passes through the point $(1,1.2)$ and is parallel to the line $\frac{x-3}{1}=\frac{y-5}{2}=\frac{z-1}{-1}.$

Answer 1

Parallel to $\frac{x-3}{1}=\frac{y-5}{2}==\frac{z-1}{-1}$
has dr'y $1,2,-1$
$P(1,-1,2)$
line is
$\frac{x-1}{1}=\frac{y+1}{2}=\frac{z-2}{-1}$
vector equals
$\overline{r}=(\hat{i}-\hat{j}+2\hat{k})+t(\hat{i}+2\hat{j}-\hat{k})$