The problem requires finding the length of the perpendicular drawn from the point $P(3, 2, 1)$ to the given line. The line is defined by a vector equation.

Given:

• Point $P(3, 2, 1)$
• The line is represented as:
  $\mathbf{r} = \mathbf{a} + \lambda \mathbf{b}$ where $\mathbf{a} = 7\mathbf{i} + 7\mathbf{j} + 6\mathbf{k}$ and ( \mathbf{b} = -2\mathbf{i} +