The cartesian equation of a line is $\frac{\large x-5}{\large 3} = \frac{\large y+4}{\large 7} = \frac{\large z-6}{\large 2}$. Write its vector form.

Question

$\begin{array}{1 1} \overrightarrow r = 5\hat i - 4\hat j + 6\hat k + t(3\hat i + 7\hat j + 2\hat k) \\ \overrightarrow r = 3\hat i +7\hat j + 2\hat k + t (5\hat i -4\hat j + 6\hat k) \\ \overrightarrow r = 5\hat i - 4\hat j + 6\hat k - t (5\hat i -4\hat j + 6\hat k) \\\overrightarrow r = 3\hat i+7\hat j + 2\hat k + t (3\hat i + 7\hat j + 2\hat k) \end{array} $