i. a = i + j + k, b = i - j + k, c = i + 2j - k
Given :
Coterminous edges of parallelopiped are \(\bar a, \bar b,\bar c\) where,
To Find : Volume of parallelepiped
Formulae :
1) Volume of parallelepiped :
If \(\bar a, \bar b,\bar c\) are coterminous edges of parallelepiped,
Where,
Then, volume of parallelepiped V is given by,
Answer :
Volume of parallelopiped with coterminous edges
= 1(-1) -1(-2) + 1(3) = -1+2+3 = 4
Therefore,
(Volume of parallelepiped = 4 cubic unit)
ii. a = -3i + 7j + 5k, b = -5i + 7j - 3k, c = 7i - 5j - 3k
Given :
Coterminous edges of parallelopiped are \(\bar a, \bar b,\bar c\) where,
To Find : Volume of parallelepiped
Formulae :
1) Volume of parallelepiped :
If \(\bar a, \bar b,\bar c\) are coterminous edges of parallelepiped,
Where,
Then, volume of parallelepiped V is given by,
Answer :
Volume of parallelopiped with coterminous edges
= -3(-36) -7(36) + 5(-24) = 108 – 252 – 120 = -264
As volume is never negative
Therefore,
(Volume of parallelepiped = 264 cubic unit)
iii. a = i - 2j + 3k, b = 2i + j - k, c = j + k
Given :
Coterminous edges of parallelopiped are \(\bar a, \bar b,\bar c\) where,
To Find : Volume of parallelepiped
Formulae :
1) Volume of parallelepiped :
If \(\bar a, \bar b,\bar c\) are coterminous edges of parallelepiped,
Where,
Then, volume of parallelepiped V is given by,
Answer :
Volume of parallelopiped with coterminous edges
= 1(2) +2(2) + 3(2) = 2 + 4 + 6 = 12
Therefore,
(Volume of parallelepiped = 12 cubic unit)
iv. a = 6i, b = 2j, c = 5k
Given :
Coterminous edges of parallelopiped are \(\bar a, \bar b,\bar c\) where,
To Find : Volume of parallelepiped
Formulae :
1) Volume of parallelepiped :
If \(\bar a, \bar b,\bar c\) are coterminous edges of parallelepiped,
Where,
Then, volume of parallelepiped V is given by,
Answer :
Volume of parallelopiped with coterminous edges
= 6(10) + 0 + 0 = 60
Therefore,
(Volume of parallelepiped = 60 cubic unit)
