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Vectors

Hot goIITian

Joined:	1 Apr 2008
Post:	124

2 Apr 2008 21:45:44 IST

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438

EXPLAIN!!!

None

(AxB).{(BxC)x(CxA)}= ?

ANS: {A.(BxC)}²

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Comments (2)

chemicaltester

Scorching goIITian

Joined: 12 Mar 2008

Posts: 233

2 Apr 2008 23:34:25 IST

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let BXC be D
CXA be f
hence
it becomes

(AXB) .{DXF}
hence it becomes
[(AXD) (.AXF) ] X [(BXD) X(BXF)]

are u sure about ur answer
mine is coming zero
or where i have mistake i dunnot knw

sreeraman nagasubramaniyan

Blazing goIITian

Joined: 17 Jan 2008

Posts: 510

3 Apr 2008 00:08:16 IST

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$a\times(b\times c) = (a.c)b - (a.b)c \\ \\ \mbox{Using this} \\ \\ (B\times C)\times(C\times A) = [(B\times C).(A)]C - [(B\times C).C]A \\ \\ \mbox{Second term is 0(bcos taking dot product with perp vector)} \\ \\ \mbox{Thus} \ (B\times C)\times(C\times A) = [(A).(B\times C)]C \\ \\ \mbox{Now take dot product of this with} \ (A\times B) \\ \\ \mbox{Use the fact that}\ (A.(B\times C)) = ((A\times B).C) \\ \\ \mbox{Hence the answer}$

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