To find the unit vector that is parallel to the resultant vectors, you need to add the sum of i, j and k components. Therefore, A= i+4j-2k and B=3i-5j+k will be
(1+3)i + (-5 +4) j + (1-2) k to get 4i -j - k. Then, find the magnitude of the vectors to get ?(4)? + (-1)? + (-1)? = 16 + 1+ 1 = 18. Then divide the value with the magnitude to get (1/?18) (4i -j - k). Learn more from http://www.eng.auburn.edu/~marghitu/MECH2110/c1_2110.pdf.