Find the volume of the parallelepiped whose conterminous edges are represented by the vectors
i. 
ii. 
iii. 
iv. 
i. 
Given :
Coterminous edges of parallelopiped are 
where,
To Find : Volume of parallelepiped
Formulae :
1) Volume of parallelepiped :
If 
are coterminous edges of parallelepiped,
Where,
Then, volume of parallelepiped V is given by,
2) Determinant :
Answer :
Volume of parallelopiped with coterminous edges
= 1(-1) -1(-2) + 1(3)
= -1+2+3
= 4
Therefore,
ii. 
Given :
Coterminous edges of parallelopiped are 
where,
To Find : Volume of parallelepiped
Formulae :
1) Volume of parallelepiped :
If 
are coterminous edges of parallelepiped,
Where,
Then, volume of parallelepiped V is given by,
2) Determinant :
Answer :
Volume of parallelopiped with coterminous edges
= -3(-36) -7(36) + 5(-24)
= 108 – 252 – 120
= -264
As volume is never negative
Therefore,
iii. 
Given :
Coterminous edges of parallelopiped are 
where,
To Find : Volume of parallelepiped
Formulae :
1) Volume of parallelepiped :
If 
are coterminous edges of parallelepiped,
Where,
Then, volume of parallelepiped V is given by,
2) Determinant :
Answer :
Volume of parallelopiped with coterminous edges
= 1(2) +2(2) + 3(2)
= 2 + 4 + 6
= 12
Therefore,
iv. 
Given :
Coterminous edges of parallelopiped are 
where,
To Find : Volume of parallelepiped
Formulae :
1) Volume of parallelepiped :
If 
are coterminous edges of parallelepiped,
Where,
Then, volume of parallelepiped V is given by,
2) Determinant :
Answer :
Volume of parallelopiped with coterminous edges
= 6(10) + 0 + 0
= 60
Therefore,
