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```
if a b c be three non-coplanar vectors and r be any arbitrary vector then (a×b)×(r×c)+(b×c)×(r×a)+(c×a)×(r×b) is equal to (1)0 (2)[a b c]r (3)2[a b c]r (4)3[a b c]r

```
2 years ago

```							Dear Akshat we have (a x b) x (r x c)= ((a x b ) . c) r – ((a x b) . r) c = [a b c] r – [a b r] csimilarly(b x c) x (r x a) = [b c a] r – [b c r] c and (c x a) x (r x b) = [c a b] r – [c a r] b when we add all three we get3 [a b c] r  –  [a b c] r = 2 [a b c] rhence option 3 is correct reagrdsArun (askIITians forum expert)
```
2 years ago 605 Points
```							Dear student,Please find the solution to your problem. we have,(a x b) x (r x c)= ((a x b ) . c) r – ((a x b) . r) c = [a b c] r – [a b r] csimilarly(b x c) x (r x a) = [b c a] r – [b c r] cand (c x a) x (r x b) = [c a b] r – [c a r] bwhen we add all threewe get3 [a b c] r  –  [a b c] r = 2 [a b c] rhence option 3 is correct Thanks and regards,Kushagra
```
2 months ago
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### Course Features

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• Revision Notes
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