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Let `overset(to)(u),overset(to)(v) " and " overset(to)(W)` be vectors such that `overset(to)(u)+overset(to)(v)+overset(to)(W)=overset(to)(0).` If `|overset(to)(u)|=3.|overset(to)(V)|=4" and " |overset(to)(W)|=5 " then " overset(to)(u).overset(to)(v)+overset(to)(v).overset(to)(w)+overset(to)(w).overset(to)(u)` is

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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)

If vectors overset(to)(a) , overset(to)(b) , overset(to)( C) are coplanar then show that |{:(overset(to)(a),,overset(to)(b),,overset(to)(c )),(overset(to)(a)"."overset(to)(a),,overset(to)(a)"."overset(to)(b),,overset(to)(a)"."overset(to)(c )),(overset(to)(b)"."overset(to)(a),,overset(to)(b)"."overset(to)(b),,overset(to)(b)"." overset(to)(c )):}|

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

For any three vectors overset(to)(a), overset(to)(b) " and " overset(to)(C ) (overset(to)(a) - overset(to)(b)). {(overset(to)(b)-overset(to)(c))xx(overset(to)(c)-overset(to)(a))} = 2overset(to)(a).(overset(to)(b)xx overset(to)(c))

For any three vectors overset(to)(a), overset(to)(b) " and " overset(to)(C ) (overset(to)(a) - overset(to)(b)). {(overset(to)(b)-overset(to)(c))xx(overset(to)(c)-overset(to)(a))} = 2overset(to)(a).(overset(to)(b)xx overset(to)(c))

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

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

Let overset(to)(a),overset(to)(b),overset(to)(c ) be unit vectors such that overset(to)(a)+overset(to)(b)+overset(to)(c ) = overset(to)(0). Which one of the following is correct ?

Let overset(to)(a),overset(to)(b),overset(to)(c ) be unit vectors such that overset(to)(a)+overset(to)(b)+overset(to)(c ) = overset(to)(0). Which one of the following is correct ?