Evaluate :
`( overline(a) + overline(b) + overline(c) )^2 =`

If overline(a) and overline(b) are parallel vectors [[overline(a), overline(b), overline(c)]] =

If overline(a), overline(b) and overline(c) are unit vectors perpendicular to each other, the [[overline(a), overline(b), overline(c)]]^(2)=

If overline(b)=2hat(i)+hat(j)-hat(k), overline(c)=hat(i)+3hat(k) and overline(a) is a unit vectors, then the maximum value of [[overline(a), overline(b), overline(c)]] is

The value of [[overline(a)-overline(b), overline(b)-overline(c), overline(c)-overline(a)]] where |overline(a)|=1, |overline(b)|=2 and |overline(c)|=3 is

The volume of paralleloP1ped with vector overline(a)+2overline(b)+overline(c), overline(a)-overline(b) and overline(a)-overline(b)-overline(c) is equal to k[[overline(a), overline(b), overline(c)]] . Then k=

If overline(c)=3overline(a)-2overline(b) , then [[overline(a), overline(b), overline(c)]]=

If overline(a), overline(b), overline(c) are linearly independent, the ([[2overline(a)+overline(b), 2overline(b)+overline(c), 2overline(c)+overline(a)]])/([[overline(a), overline(b), overline(c)]])=

If overline(p)=(overline(b)timesoverline(c))/([[overline(a), overline(b), overline(c)]]), overline(q)=(overline(c)timesoverline(a))/([[overline(a), overline(b), overline(c)]]), overline(r)=(overline(a)timesoverline(b))/([[overline(a), overline(b), overline(c)]]) , where overline(a), overline(b), overline(c) are three non-coplanar vectors, then (overline(a)-overline(b)-overline(c))*overline(p)-(overline(b)-overline(c)-overline(a))*overline(q)-(overline(c)-overline(a)-overline(b))*overline(r)=