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Let vec(C )= vec(A)+vec(B) then...

Let `vec(C )= vec(A)+vec(B)` then

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Let vec(a), vec(b), vec(c) be non-coplanar vectors and vec(p)=(vec(b)xxvec(c))/([vec(a)vec(b)vec(c)]), vec(q)=(vec(c)xxvec(a))/([vec(a)vec(b)vec(c)]), vec(r)=(vec(a)xxvec(b))/([vec(a)vec(b)vec(c)]) . What is the value of (vec(a)-vec(b)-vec(c)).vec(p)+(vec(b)-vec(c)-vec(a)).vec(q)+(vec(c)-vec(a)-vec(b)).vec(r) ?

Let vec(a), vec(b), vec(c) be vectors of length 3, 4, 5 respectively. Let vec(a) be perpendicular to vec(b)+vec(c), vec(b) to vec(c)+vec(a) and vec(c) to vec(a)+vec(b) . Then |vec(a)+vec(b)+vec(c)| is :

Let vec(a), vec(b), vec(c) be vectors of length 3, 4, 5 respectively. Let vec(a) be perpendicular to vec(b)+vec(c), vec(b) to vec(c)+vec(a) and vec(c) to vec(a)+vec(b) . Then |vec(a)+vec(b)+vec(c)| is :

Let vec(a), vec(b), vec(c) be vectors of length 3, 4, 5 respectively. Let vec(a) be perpendicular to vec(b)+vec(c), vec(b) to vec(c)+vec(a) and vec(c) to vec(a)+vec(b) . Then |vec(a)+vec(b)+vec(c)| is :

Let vec(a), vec(b), vec(c) be vectors of length 3, 4, 5 respectively. Let vec(a) be perpendicular to vec(b)+vec(c), vec(b) to vec(c)+vec(a) and vec(c) to vec(a)+vec(b) . Then |vec(a)+vec(b)+vec(c)| is :

Let vec(a), vec(b), vec(c ) be such that vec(c ) ne vec(0), vec(a) xx vec(b)= vec(c ) and vec(b) xx vec(c )= vec(a) then show that vec(a), vec(b) and vec(c ) are pairwise perpendicular, |vec(b)|=1 and |vec(c )|= |vec(a)| .

Let vec(a), vec(b) and vec(c) be three vectors such that vec(a) + vec(b) + vec(c) = 0 and |vec(a)|=10, |vec(b)|=6 and |vec(c) |=14 . What is the angle between vec(a) and vec(b) ?

Let vec(a), vec(b) and vec(c) be three vectors such that vec(a) + vec(b) + vec(c) = 0 and |vec(a)|=10, |vec(b)|=6 and |vec(c) |=14 . What is vec(a). vec(b) + vec(b).vec(c)+ vec(c). vec(a) . equal to ?