If ^a, ^b, and ^c are mutually perpendicular unit vectors, then find the value of |2^a + ^b + ^c|.

|2^a + ^b + ^c| represents the distance between the points (0, 0, 0) and (2, 1, 1) in the (^a, ^b, ^c) space. Thus, by the distance formula, we have |2^a + ^b + ^c| = √(2² + 1² + 1²) = √6.