Question

Find the volume of the parallelepiped determined by the vectors →a=〈4,2,−1〉a→=〈4,2,-1〉, →b=〈0,3,4〉b→=〈0,3,4〉, →c=〈2,3,1〉c→=〈2,3,1〉.

Answer 1

The given vectors are

Recall that the volume of a parallelepiped determined by the vectors is given by the absolute value of their triple scalar product, i.e.

When expanded ,the inside of the right hand side becomes

where are the components of the vectors respectively.

Plug in the values and evaluate:

Hence, the required volume is