# Thread: Cross product of 3 vectors:

1. ## Cross product of 3 vectors:

This is somewhat of a conceptual question that I need resolved as I may have interpreted things wrong:

When we have two vectors, U and V, taking their cross products (UxV) produces a resultant vector that is orthogonal to both U and V.

Now if we consider a 3 by 3 matrix in which each row would represent a vector, respectively U, V, W. If we compute the wronskian of the matrix is the resulting vector orthogonal to U, V and W?

If no could you please clarify why and is there a way to compute a cross product of 3 or more vectors? (possibly by introducing higher dimensions)

Thank you for the help.

2. Originally Posted by Armen

If no could you please clarify why and is there a way to compute a cross product of 3 or more vectors? (possibly by introducing higher dimensions)
.
Because the matrix in the first row is composed of the elements of the n-dimensional vector space. The second rule is composed of n-unique elements required for a linear combination and the same for the thirds row. In total you have 3 rows and n elements in each row. In order to compute the determinant we need that n=3. Thus it cannot work for anything more than 3.

3. Originally Posted by Armen
This is somewhat of a conceptual question that I need resolved as I may have interpreted things wrong:

When we have two vectors, U and V, taking their cross products (UxV) produces a resultant vector that is orthogonal to both U and V.

Now if we consider a 3 by 3 matrix in which each row would represent a vector, respectively U, V, W. If we compute the wronskian of the matrix is the resulting vector orthogonal to U, V and W?
I don't know what you mean by the Wronskian in this context - it is
usualy defined for a set of functions.

If no could you please clarify why and is there a way to compute a cross product of 3 or more vectors? (possibly by introducing higher dimensions)
Look at the definition of the wedge product in the section on higher dimensions at this link

RonL

4. K the links you provided has the information I need thank you for the help.