Question

The vector equation of the line passing through the points (3, 4, –7) and (1, –1, 6) is _______________.

Answer 1

Since vector equation of a line passing through $\overrightarrow{a}\mathrm{and}\overrightarrow{b}$is

$$\begin{gathered} \overrightarrow{r}=\overrightarrow{a}+\lambda \left(\overrightarrow{b}-\overrightarrow{a}\right) \\ \mathrm{here}\overrightarrow{a}=\left(3,4,-7\right)\mathrm{and}\overrightarrow{b}=\left(1,-1,6\right) \\ \therefore \mathrm{Vector}\mathrm{equation}\mathrm{is}\mathrm{given}\mathrm{by} \\ \overrightarrow{r}=\left(3\hat{i}+4\hat{j}-7\hat{k}\right)+\lambda \left\{\left(1-3\right)\hat{i}+\left(-1-4\right)\hat{j}+\left(6+7\right)\hat{k}\right\} \\ \mathrm{i}.\mathrm{e}.\overrightarrow{r}=3\hat{i}+4\hat{j}-7\hat{k}+\lambda \left(-2\hat{i}-5\hat{j}+13\hat{k}\right) \end{gathered}$$