Line `L_(1)` is parallel to vector `vec(alpha) = - 3hati + 2hatj+ 4hatk` and passes through a point A(7, 6, 2) and line `L_(2)` is parallel to a vector `vec(beta) = 2hati + 2hatj + 3hatk` and passes through a point B(5,3,4). Now a line `L_(3)` parallel to a vector `vec(r) = 2hati - 2hatj - hatk` intersects the line `L_(1)` and `L_(2)` at point C and D respectively, Find `|vec(CD)|`.