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               The vector equation of the line that passes through the points (3, 4, -7) and (1, -1, 6) is ______.

Answers (1)

The position vector of the first point (3, 4, -7) is  \vec{a}=3\hat{i}+4\hat{j}-7\hat{k}

And the position vector of the second point(1, -1, 6): \vec{b}=\hat{i}-\hat{j}+6\hat{k}

Also, the vector equation of a line passing through two points with position vectors a and b is given by:

\vec{r}=\vec{a}+\lambda\left ( \vec{b}-\vec{a} \right )

Thus, the required line equation is

\vec{r}=3\hat{i}+4\hat{j}-7\hat{k}+\lambda\left ( \hat{i}-\hat{j}+6\hat{k}-\left ( 3\hat{i}+4\hat{j}-7\hat{k} \right ) \right )

\vec{r}=3\hat{i}+4\hat{j}-7\hat{k}+\lambda\left ( -2\hat{i}-5\hat{j}+13\hat{k} \right )

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