Find the cartesian equation of the line that passes through the point with position vector \( \hat{i}+2\hat{j}+\hat{k}\) and is in the direction of the vector \( \hat{i}-2\hat{j}+3\hat{k}\) ?
1
\(\frac{x-1}{1}=\frac{y-2}{-2}=\frac{z-1}{3}\)
2
\(\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-1}{3}\)
3
\(\frac{x-1}{1}=\frac{y+2}{-2}=\frac{z-1}{3}\)
4
\(\frac{x-1}{1}=\frac{y+2}{2}=\frac{z-3}{1}\)