Solution :
We know that the vector equation of line passing through two points with position vectors \(\vec{a}\) and \(\vec{b}\) is,
\(\vec{r}\) = \(\lambda\) \((\vec{b} – \vec{a})\)
Here \(\vec{a}\) = \(3\hat{i} + 4\hat{j} – 7\hat{k}\) and \(\vec{b}\) = \(\hat{i} – \hat{j} + 6\hat{k}\).
So, the vector equation of the required line is
\(\vec{r}\) = (\(3\hat{i} + 4\hat{j} – 7\hat{k}\)) + \(\lambda\) (\(\hat{i} – \hat{j} + 6\hat{k}\) – \(3\hat{i} + 4\hat{j} – 7\hat{k}\))
or, \(\vec{r}\) = (\(3\hat{i} + 4\hat{j} – 7\hat{k}\)) + \(\lambda\) (\(-2\hat{i} – 5\hat{j} + 13\hat{k}\))
where \(\lambda\) is a scalar.
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