Determine the vector equation for the line, given the cartesian equation of a line is \(\frac{{x + 5}}{3} = \frac{{y - 7}}{2} = \frac{{z + 3}}{2}\)?
1
\(\overrightarrow r = (-3\hat i + 5\hat j - 6\widehat k) + \lambda (2\hat i + 4\hat j + 2\widehat k)\)
2
\(\overrightarrow r = (-5\hat i + 7\hat j - 3\widehat k) + \lambda (2\hat i + 4\hat j + 2\widehat k)\)
3
\(\overrightarrow r = (-5\hat i + 7\hat j - 3\widehat k) + \lambda (3\hat i + 2\hat j + 2\widehat k)\)
4
\(\overrightarrow r = (-3\hat i + 5\hat j - 6\widehat k) + \lambda (3\hat i + 2\hat j + 2\widehat k)\)