Prove that for any three vectors a- b- and c- -a- - b- b- - c- c- - a- - 2-a- b- c-

LHS: [(a⃗+b⃗) #160;(b⃗+c⃗) #160; #160;(c⃗+a⃗)] =(a⃗+b⃗). [ b⃗+c⃗×c⃗+a⃗ ] =(a⃗+b⃗). [ b⃗×c⃗+b⃗×a⃗+c⃗×c⃗+c⃗×a⃗ ] =a⃗.(b⃗×c⃗)+b⃗.(c⃗×a⃗ ...

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Work Done as Dot Product

Prove that fo...

Question

Prove that for any three vectors $\to a, \to b$ and $\to c,$ $[(\to a + \to b) (\to b + \to c) (\to c + \to a)] = 2 [\to a \to b \to c] .$

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\to a, \to b, \to c

[\to a + \to b \to b + \to c \to c + \to a]

\to a, \to b a n d \to c

[\to a + \to b \to b + \to c \to c + \to a] =

\to a, \to b, \to c

\to a, \to b, \to c

\to a \times \to b = \to b \times \to c = \to c \times \to a

[\to a \to b \to c] = 0.

\to a, \to b, \to c

\to a + \to b + \to c = \to 0,

\to a \times \to b = \to b \times \to c = \to c \times \to a,

[\to a \to b \to c] = 0.

\frac{[(\to a \times \to b) \times (\to b \times \to c) (\to b \times \to c) \times (\to c \times \to a) (\to c \times \to a) \times (\to a \times \to b)]}{[\to a \times \to b \to b \times \to c \to c \times \to a]}

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