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,