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Joint Entrance Examination
Mathematics
Vector Algebra
Question 376
Question 376 of 379
Easy
MCQ
If
a
⃗
,
b
⃗
,
c
⃗
\vec a,\vec b,\vec c
a
,
b
,
c
are vectors such that
[
a
⃗
b
⃗
c
⃗
]
=
4
[\vec a\ \vec b\ \vec c]=4
[
a
b
c
]
=
4
, then
[
(
a
⃗
×
b
⃗
)
(
b
⃗
×
c
⃗
)
(
c
⃗
×
a
⃗
)
]
=
[(\vec a\times\vec b)\ (\vec b\times\vec c)\ (\vec c\times\vec a)]=
[(
a
×
b
)
(
b
×
c
)
(
c
×
a
)]
=
A
16
B
64
C
4
D
8
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Official solution
By the standard identity
[
(
a
⃗
×
b
⃗
)
(
b
⃗
×
c
⃗
)
(
c
⃗
×
a
⃗
)
]
=
[
a
⃗
b
⃗
c
⃗
]
2
=
4
2
=
16
[(\vec a\times\vec b)\ (\vec b\times\vec c)\ (\vec c\times\vec a)]=[\vec a\ \vec b\ \vec c]^2 = 4^2=16
[(
a
×
b
)
(
b
×
c
)
(
c
×
a
)]
=
[
a
b
c
]
2
=
4
2
=
16
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