If `overset(to)(V) = 2oveset(to)(i) + overset(to)(j) - overset(to)(k) " and " overset(to)(W) = overset(to)(i) + 3overset(to)(k) .` if `overset(to)(U)` is a unit vectors then the maximum value of the scalar triple product `[overset(to)(U) , overset(to)(v) , overset(to)(W)]` is

The projection of the vector overset(^)(i) - 2 overset(^)(j) + overset(^)(k) on the vector 4 overset(^)(i) 4 overset(^)(j) + 7 overset(^)(k) 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 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

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

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

The projection of the vector 2overset(^)(i)+overset(^)(j)-3overset(^)(k) on the vector overset(^)(i)-2overset(^)(j)+overset(^)k is...

If the vectors overset(^)i+2overset(^)k,overset(^)j+overset(^)k and lambda overset(^)i+mu overset(^)j collinear, then