Vector Algebra

A line $L_1$ passing through the point A with position vector $\vec{a}=4 \hat{i}+2 \hat{j}+2 \hat{k}$ is parallel to the vector $\vec{b}=2 \hat{i}+3 \hat{j}+6 \hat{k}$. The length of the perpendicular drawn from a point P with position vector $\vec{p}=\hat{i}+2 \hat{j}+3 \hat{k}$ to $L_1$ is