In axbxc, if all the vectors parallel or if b and c are parallel or if a is parallel to bxc or a is perpendicular to the plane defined by b and c, then the vector triple product will be a null vector. In section 3, the scalar triple product and vector triple product are introduced, and the fundamental identities for each triple product are discussed and derived. Ollscoil na heireann ma nuad the national university of. Proof of the vector triple product equation on page 41. If you are unfamiliar with matrices, you might want to look at the page on matrices in the algebra section to see how the determinant of a threebythree matrix is found. Vector product a x b has c cos magnitude equal to the area of the base direction perpendicular to the base. To remember the formulas for the two vector triple products, there is a quick way. Geometrical interpretation of scalar triple product 2. The dot product of the first vector with the cross product. Vector triple product 0 mathematics stack exchange.
For this reason it is vital that we include the parentheses in a vector triple product to indicate which vector product should be performed first. The triple scalar product produces a scalar from three vectors. Vector triple product definition, examples and more. You see that the nal product of the rst vector triple product will be perpendicular to a b, so it will lie in the plane spanned by a and b. It is perpendicular to c,so there will be no component in the c direction. It is the result of taking the cross product of one vector with the cross product of two other vectors. We now obtain a formula for the vector triple product which reflects the fact that u. There are many more uses as well like the scalar triple product, vector triple product and so on. Triple products, multiple products, applications to geometry 3. Vector triple product an overview sciencedirect topics. Both the scalar and vector products of two vectors are used to check the coplanarity of vectors. Below is the actual calculation for finding the determinant of the above matrix i. A b c acb abc proving the vector triple product formula can be done in a number of ways. Revision of vector algebra, scalar product, vector product 2.
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