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Question
Mathematics
If vec a and vec b are perpendicular, then vec a ×( vec a ×( vec a ×( vec a × vec b ))) is equal to
Q. If
a
and
b
are perpendicular, then
a
×
(
a
×
(
a
×
(
a
×
b
)))
is equal to
4733
250
JEE Main
JEE Main 2021
Vector Algebra
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A
0
40%
B
2
1
∣
a
∣
4
b
11%
C
a
×
b
16%
D
∣
a
∣
4
b
32%
Solution:
a
⋅
b
=
0
a
×
(
a
×
b
)
=
(
a
⋅
b
)
a
−
(
a
⋅
a
)
b
=
−
∣
a
∣
2
b
Now
a
×
(
a
×
(
−
∣
a
∣
2
b
)
)
=
−
∣
a
∣
2
(
a
×
(
a
×
b
))
=
−
∣
a
∣
2
(
−
∣
a
∣
2
b
)
=
∣
a
∣
4
b