A trick for right-handed coordinate systems to find out which way the cross product of two 3-vectors will be directed. There are few forms of this rule, and this can be applied in several ways. If u & v are two vectors that are not parallel, then u cross v is a vector that is directed in the following way: Orient your right hand so that your thumb remain perpendicular to the plane described by the vectors u & v. If you can curl your fingers into the direction from vector u to vector v, your thumb will point out in the direction of u cross v. (If it doesn't, the vector is directed into the opposite direction.) It has immediate application for finding out the orientation of the z-axis basis unit vector, k, in terms of the x- & y-axes' basis unit vectors; curl your right hand into the direction of i to j, and your thumb will point out into the direction of i cross j = k.
The rule is also applicable in many practical applications, like determining which way to turn a screw, etc. There is also a left-hand rule that exhibits opposite chirality.