For any three vectors a- b- and c- prove that -a- - b- b- - c- c- - a- - 2-a-b-c- Hence prove that the vectors a- -b- b- - c- c- - a- are coplanar- If and only if a-b-c- are coplanar-

#10; #10; [(a⃗+b⃗).(b⃗+c⃗),(c⃗+a⃗)] =(a⃗+b⃗).[(b⃗+c⃗)×(c⃗+a⃗)] =(a⃗+b⃗).[b⃗×c⃗+b⃗×a⃗+c⃗×c⃗+c⃗×a⃗ #10;] =(a⃗+b⃗).(b⃗×c⃗+b⃗×a⃗+c⃗×a⃗) = ...

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Collinear Vectors

For any three...

Question

For any three vectors $\to a, \to b$ and $\to c$ , prove that $[\to a + \to b, \to b + \to c, \to c + \to a] = 2 [\to a \to b \to c]$ . Hence prove that the vectors $\to a + \to b, \to b + \to c, \to c + \to a$ are coplanar. If and only if $\to a, \to b, \to c$ are coplanar.

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