Question

Find the vector equation of the line passing through the points $2\hat{i}+3\hat{j}+\hat{k}$ and parallel to the vector $4\hat{i}-2\hat{j}+3\hat{k}$ .

Answer 1

Consider the problem

Let,

$\begin{array}{c}\overrightarrow{a}=2\hat{i}+3\hat{j}+\hat{k}\\ \\ \overrightarrow{b}=4\hat{i}-2\hat{j}+3\hat{k}\end{array}$

Therefore, vector equation of the line is

$\overrightarrow{r}=\overrightarrow{a}+\lambda \overrightarrow{b}$

because the line is passing through point A and is parallel to line B

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