To find the direction of a given vector, we have to find the unit vector in the direction of given vector.
Let a=i^+2j^+3k^
Then, ∣a∣=12+22+32=14 ∴a^=∣a∣a⇒a^=141(i^+2j^+3k^) ⇒a^=141i^+142j^+143k^
Hence, direction cosines of the given vector are 141,142,143 (∵ direction cosines are the coefficients of i^,j^,k^ of unit vector).