# Find the volume of the parallelepiped

• chwala
In summary, the conversation discusses the use of a form in vector calculus and its relation to the dot product and cross product. The form ##[i×j=k, k×i=j , j×k=i]## is not applicable in this context and the conversation also touches on the concept of interchanging rows in a determinant.

#### chwala

Gold Member
Homework Statement
see attached
Relevant Equations
vector calculus
Am refreshing on this; see attached below

ok we can also use the form ##[i×j=k, k×i=j , j×k=i]## right?

to give us say, ##w⋅(u ×v)=v⋅(w ×u)## in realizing same solution.

Please elaborate on what you mean by "the form ##[i×j=k, k×i=j , j×k=i]##".

I wanted to indicate,
For any vectors in 3-dimensional space it follows that,
##w⋅(u ×v)=v⋅(w ×u)=u⋅(v ×w)##... yap with this, i should realize the same value of the required volume... the form ##[i×j=k, k×i=j , j×k=i]## is not applicable here...

chwala said:
the form ##[i×j=k, k×i=j , j×k=i]## is not applicable here...