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Find the vector equation of the line which passes through the point (3, 4, 5) and is parallel to the vector $2\hat{i}+2\hat{j}-3\hat{k}$ .

Answers (1)

R Ravindra Pindel

Given the line passes through a point $(3,4,5)$ and parallel to vector $2\hat{i}+2\hat{j}-3\hat{k}$

Direction ratios are $(2,2,-3)$

$\therefore$ Vector equation of the line : $\vec{r}=\vec{a}+\lambda \vec{b}$

$\vec{b}=2\hat{i}+2\hat{j}-3\hat{k}$

$\vec{a}=3\hat{i}+4\hat{j}+5\hat{k}$

$\therefore \vec{r}=(3\hat{i}+4\hat{j}+5\hat{k})+\lambda (2\hat{i}+2\hat{j}-3\hat{k})$

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