Question
Find the vector equation of the line which passes through the point with position vector $4 \bar{i}-\bar{j}+2 \hat{k}$ and is in the direction of $-2 \bar{i}+\bar{j}+\hat{k}$.
Let $\bar{a}=4 \hat{i}-\hat{j}+2 \widehat{k}$
$\bar{b}=-\hat{2} i+\hat{j}+\widehat{k}$
Equation of the line passing through point $A(\bar{a})$ and having direction $\bar{b}$ is
$\bar{r}=\bar{a}+\lambda \bar{b}$
$\bar{r}=(4 \hat{i}-\hat{j}+2 \widehat{k})+\lambda(-2 \hat{i}+\hat{j}+\widehat{k})$
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