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Question

If a,b,c are any three vectors such that (a+b).c=(ab).c=0 then (a×b)×c is

A
0
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B
a
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C
b
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D
none of these
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Solution

The correct option is A 0
(ab).c
=a.cbc
=0
Hence
a.c=b.c
Now
c×(a×b)
=[a(c.b)b(c).(a)]
=[a(c.b)b(b).(c)]
=0

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