Find the equation of the line which passes through the point $(1, 2, 3)$ and is parallel to the vector $3\hat{i} + 2\hat{j} -2\hat{k}$. .

Question

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