To find a vector that is perpendicular to two given vectors, the cross product of the two vectors should be calculated. For vectors A(1,-1,2) and B(2,1,-3), the cross product A x B yields a vector that is perpendicular to both. To convert this resultant vector into a unit vector, divide it by its norm. Understanding how to compute the cross product is essential for this process. This method effectively identifies perpendicular vectors in three-dimensional space.