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If you know the direction of the tool's approach vector then yes you can use the cross product to "produce" the other two orthogonal vectors needed to define an orthonormal 3x3 orientation matrix. The 3x3 orientation matrix R can be represented as R = [tx ty tz] where each entry is a 3x1 unit vector and all vectors are perpendicular to each other. Assuming that the known tool vector [a,b ,c] is the tz vector then you can obtain tx as the cross product of tz and [0 1 0]' . Then ty is just the cross product between tz and tx. You can then form the matrix R. The Eigen library has very powerful tools for doing these sort of calculations and its well integrated into MoveIt!