Question

Find the equation of line passing through points
(i) $(3\hat{i}+2\hat{j}-8\hat{k})$,$(5,2,-4)$

Answer 1

Given two points $\to (3,2,-8)\&(5,2,-4)$

Direction ratios $\to (5-3),(2-2),(-4-(-8\left)\right)$

$\to (2,0,4)$

So, vector equation of a line we can write as

$\overrightarrow{r}={\overrightarrow{x}}_1+\lambda \overrightarrow{d}$

$\overrightarrow{r}=(3\hat{i}+2\hat{j}-8\hat{k})+\lambda (2\hat{i}+4\hat{k})$