Find the volume of the parallelepiped whose coterminous edges are represented by the vector: ` vec a=2 hat i+3 hat j+4 hat k ,\ vec b= hat i+2 hat j- hat k ,\ vec c=3 hat i- hat j+2 hat k` .

Options

A. 21 cubic units
B. 14 cubic units
C. 7 cubic units
D. none of these

Answer

C

Explanation

We have
`(vec(a)xxvec(b)).vec(c)=|(2,-3,4),(1,2,-1),(3,-1,2)|=2(4-1)+3(2+3)+4(-1-6)`
`=(6+15-28)=-7`.
`:.` volume of the parallelopiped
`=|(vec(a)xxvec(b)).vec(c)|=|-7|=7` cubic units.