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A,B,C and d are four points in a pla...

A,B,C and d are four points in a plane with position vectors `overset(to)(a),overset(to)(b),overset(to)(c )` and `overset(to)(d)` respectively such that `(overset(to)(a)-overset(to)(d)).(overset(to)(b)-overset(to)(c))=(overset(to)(b)-overset(to)(d))(overset(to)(c)-overset(to)(a))=0` The point D then is the .... of the `DeltaABC`

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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 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