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

Given a⃗ ,b⃗ ,c⃗ are three vectors such that a⃗×b⃗ =b⃗×c⃗ =c⃗×a⃗ Consider a⃗×b⃗ =b⃗×c⃗ , ⟹( a⃗×b⃗ #160; ) .c⃗ =( b⃗×c⃗ #160; ) .c⃗ ⟹ ...

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If a⃗ ,b⃗ ,...

Question

If $\to a, \to b, \to c$ are three vectors such that $\to a, \to b, \to c$ , 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 0,

\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 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 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] = 5

[\to a \times \to b, \to b \times \to c, \to c \times \to a]

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