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if overset(to)(a), overset(to)(b) " and ...

if `overset(to)(a), overset(to)(b) " and " overset(to)(c )` are unit vectors satisfying
`|overset(to)(a)-overset(to)(b)|^(2)+|overset(to)(b)-overset(to)(c)|^(2)+|overset(to)(c)-overset(to)(a)|^(2)=9`
`|2overset(to)(a) +5overset(to)(b)+5overset(to)(c)|` is equal to

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if overset(to)(a),overset(to)(b) " and " overset(to)(c ) are unit vectors then |overset(to)(a)-overset(to)(b)|^(2)+|overset(to)(b)-overset(to)c|^(2)+|overset(to)(c)-overset(to)(a)|^(2) does not exceed

If overset(to)(a) , overset(to)(b) " and " overset(to)( c) are unit coplanar vectors then the scalar triple product [2 overset(to)(a) - overset(to)(b) 2 overset(to)(b) - overset(to)(c ) 2 overset(to)(c ) - overset(to)(a)] is

If overset(to)(a) , overset(to)(b) " and " overset(to)( c) are unit coplanar vectors then the scalar triple product [2 overset(to)(a) - overset(to)(b), 2 overset(to)(b) - overset(to)(c ) ,2 overset(to)(c ) - overset(to)(a)] is

If overset(to)(a) , overset(to)(b) " and " overset(to)(c ) are three non- coplanar vectors then (overset(to)(a) + overset(to)(b) + overset(to)(c )) . [( overset(to)(a) + overset(to)(b)) xx (overset(to)(a) + overset(to)(c ))] equals

If overset(to)(a) , overset(to)(b) " and " overset(to)(c ) are three non- coplanar vectors then (overset(to)(a) + overset(to)(b) + overset(to)(c )) . [( overset(to)(a) + overset(to)(b)) xx (overset(to)(a) + overset(to)(c ))] equals

For any three vectors overset(to)(a) , overset(to)(b) and overset(to) ( c ) , prove that vectors overset(to)(a) - overset(to)(b) , overset(to)(b) - overset(to) ( c), overset(to)(c) - overset(to)(a) are coplanar.

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If overset(to)(A) , overset(to)(B) " and " overset(to)( c) are vectors such that |overset(to)(B) |=|overset(to)( C ) | . Prove that | (overset(to)(A) + overset(to)(B)) xx (overset(to)(A) + overset(to)(C )) | xx (overset(to)(B) xx overset(to)(C )) . (overset(to)(B) + overset(to)( C )) = overset(to)(0)

The scalar overset(to)(A) .[(overset(to)(B) + overset(to)( C)) xx (overset(to)(A) + overset(to)(B) + overset(to)( C))] equals