If a- b- c- are three vectors such that a-b-c-0- then prove that a-b-b-c-c-a- and hence show that -a-b-c-0

Given a⃗ + b⃗ + c⃗ = 0⃗ ⇒a⃗×b⃗ = ( b⃗ c⃗) ×b⃗ = b⃗×b⃗ c⃗×b⃗ ⇒a⃗×b⃗ = 0⃗ + b⃗×c⃗ ⇒a⃗×b⃗ = b⃗×c⃗...(i) That is a⃗×b⃗ = ( a⃗ c⃗) ×c⃗ [∵a⃗ ...

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Condition for Coplanarity of Four Points

If a⃗, b⃗, c⃗...

Question

If $\to a, \to b, \to c$ are three vectors such that $\to a + \to b + \to c = \to 0,$ then prove that $\to a \times \to b = \to b \times \to c = \to c \times \to a,$ and hence show that $[\to a \to b \to c] = 0.$

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\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 \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

\to a, \to b, \to c

[\to a \to b \to c] = 4

[\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 a . \to c, \to a \times \to b = \to a \times \to c, \to a \neq 0

\to b = \to c

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