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A student claims that ( a× b)× c = a×( b× c) for all… | StemPy Lab
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A student claims that ( a× b)× c = a×( b× c) for all vectors. Which choice of vectors shows that the claim is false?
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Vectors and Three-Dimensional Geometry › Vector Algebra
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A student claims that
(
a
⃗
×
b
⃗
)
×
c
⃗
=
a
⃗
×
(
b
⃗
×
c
⃗
)
(\vec a\times\vec b)\times\vec c = \vec a\times(\vec b\times\vec c)
(
a
×
b
)
×
c
=
a
×
(
b
×
c
)
for all vectors. Which choice of vectors shows that the claim is false?
No choice works, because the claim is true
a
⃗
=
i
^
\vec a = \hat i
a
=
i
^
,
b
⃗
=
i
^
\vec b = \hat i
b
=
i
^
,
c
⃗
=
j
^
\vec c = \hat j
c
=
j
^
: the left side is
0
⃗
\vec 0
0
and the right side is
−
j
^
-\hat j
−
j
^
a
⃗
=
i
^
\vec a = \hat i
a
=
i
^
,
b
⃗
=
j
^
\vec b = \hat j
b
=
j
^
,
c
⃗
=
k
^
\vec c = \hat k
c
=
k
^
: the left side is
j
^
\hat j
j
^
and the right side is
i
^
\hat i
i
^
a
⃗
=
i
^
\vec a = \hat i
a
=
i
^
,
b
⃗
=
i
^
\vec b = \hat i
b
=
i
^
,
c
⃗
=
i
^
\vec c = \hat i
c
=
i
^
: the left side is
i
^
\hat i
i
^
and the right side is
0
⃗
\vec 0
0
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