If a-b-c-0- the prove that- a-b-b-c-c-a- where a- b- c- are non-zero vectors-

Given a⃗+b⃗+c⃗=0 #160; #160; #160; #160; ......(1)Multiplying a⃗ in both the sides. a⃗× (a⃗+b⃗+c⃗)=a⃗×0⃗ ⇒a⃗×a⃗+a⃗×b⃗+a⃗×c⃗=0⃗ ...

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Geometric Progression

If a⃗+b⃗+c⃗...

Question

If $\to a + \to b + \to c = 0$ , the prove that: $\to a \times \to b = \to b \times \to c = \to c \times \to a$ where $\to a, \to b, \to c$ are non-zero vectors.

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\to a, \to b, \to c

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

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

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

\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 =

\to a, \to b, \to c

(\to a \times \to b) \times (\to a \times \to c) + (\to b \times \to c) \times (\to b \times \to a) + (\to c \times \to a) \times (\to c \times \to b)

\to a, \to b, \to c

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

| \to a | = | \to b | = | \to c |

\to A

\to B

\to C

| \to B | =

\to C |

[(\to A + \to B) \times (\to A + \to C)] \times (\to B \times \to C) . (\to B + \to C) = 0

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