Finally, introduce the dot and cross products of screws by the formulas: S ⋅ ⋅ T = ( S , V ) ⋅ ⋅ ( T , W ) = ( S ⋅ ⋅ T , S ⋅ ⋅ W + V ⋅ ⋅ T ) , which is a dual scalar, and S × × T = ( S , V ) × × ( T , W ) = ( S × × T , S × × W + V × × T ) . which is a screw. The dot and cross products of screws satisfy the identities of vector algebra, and allow computations that directly parallel computations in the algebra of vectors.