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IIT JEE Advanced 2008 Paper 1
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© examsnet.com
Question : 52
Total: 69
The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors
^
a
,
^
b
,
^
c
such that
^
a
.
^
b
=
^
b
.
^
c
=
^
c
.
^
a
= 1/2. Then the volume of the parallelopiped is
1
√
2
1
2
√
2
√
3
2
1
√
3
Validate
Solution:
We have
^
a
.
^
a
=
^
b
.
^
b
=
^
c
.
^
c
= 1
^
a
.
^
b
=
^
b
.
^
c
=
^
c
.
^
a
= 1/2
Therefore,
[
a
b
c
]
2
=
|
a
.
a
a
.
b
a
.
c
b
.
a
b
.
b
b
.
c
c
.
a
c
.
b
c
.
c
|
=
|
1
1
2
1
2
1
2
1
1
2
1
2
1
2
1
|
=
1
2
Hence, the volume of the given parallelopiped is
[
a
b
c
]
=
1
√
2
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