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3. a (b + c) = a b + a c. The cross product distributes across vector addition, just like the dot product. Likethedotproduct,thecrossproductbehavesalotlikeregularnumbermultiplication,withtheexception ofproperty1. Thecrossproductisnotcommutative. There are a lot of other algebraic … Application of cross product and dot product Clareview For vectors and , the dot product is . The cross product is a vector orthogonal to three-dimensional vectors and , and can be used to determine the area or volume of a parallelogram defined by , , and . For vectors and , the cross product is , which is the determinate of a three-by-three matrix.