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A.( B× ( C× ( B.(A×c)))= ?
A,B,C are vectors
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By def a.b = ab CosA, where is A is angle between vectors a, b where
|a| = a and |b| = b
So we find a.b first & compare it with ab.
Note a.a = a^2 = square of length of a
c^2 = c.c = (a+b).(a+b) = a^2+b^2+2a.b (Since a+b = c)
c^2 = (a+b)^2 => a^2+b^2+2ab (since a+b = c)
=> c^2 = a^2+b^2+2a.b = a^2+b^2+2ab
=> a.b = ab => ab cosA = ab => cos A = 1 => A = 0, pi, 2pi etc.,
|a| = a and |b| = b
So we find a.b first & compare it with ab.
Note a.a = a^2 = square of length of a
c^2 = c.c = (a+b).(a+b) = a^2+b^2+2a.b (Since a+b = c)
c^2 = (a+b)^2 => a^2+b^2+2ab (since a+b = c)
=> c^2 = a^2+b^2+2a.b = a^2+b^2+2ab
=> a.b = ab => ab cosA = ab => cos A = 1 => A = 0, pi, 2pi etc.,
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