Please only answer if you are 100% sure Please answer with details Q1: prove tha

Question

Please only answer if you are 100% sure Please answer with details
Q1: prove that Ax(BxC)+Cx(AxB)=0
Where A, B, and C are three vectors

Q2: carry out the integration of ( x^(2) y+y^(2) x) on the following loop: (x=1, y=2) -> (x=2, y=1) -> (x=3, y=3) -> (x=1, y=2) Please only answer if you are 100% sure Please answer with details
Q1: prove that Ax(BxC)+Cx(AxB)=0
Where A, B, and C are three vectors

Q2: carry out the integration of ( x^(2) y+y^(2) x) on the following loop: (x=1, y=2) -> (x=2, y=1) -> (x=3, y=3) -> (x=1, y=2) Please answer with details
Q1: prove that Ax(BxC)+Cx(AxB)=0
Where A, B, and C are three vectors

Q2: carry out the integration of ( x^(2) y+y^(2) x) on the following loop: (x=1, y=2) -> (x=2, y=1) -> (x=3, y=3) -> (x=1, y=2)

Explanation / Answer

(1) L.H.S = a x (b x c) + b x (c x a) + c x (a x b) =

= (a.c)b - (a.b)c + (b.a)c - (b.c)a + (c.b)a - (c.a)b (using identity of cross-product)

= (a.c)b - (a.b)c + (a.b)c - (b.c)a + (b.c)a - (a.c)b [Since dot product of two vectors is commutative]

= 0 [corresponiding products cancels out] =R.H.S

Hence it is proved that, a x (b x c) + b x (c x a) + c x (a x b) = 0.

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