Let `vec(a),vec(b)` and `vec( c )` be three vectors such that `|vec(a)|=3,|vec(b)|=4,|vec( c )|=5` and each one the them being perpendicular to the sum of the other two, find `|vec(a)+vec(b)+vec( c )|`.

For the vectors vec(a),vec(b) and vec( c ),|vec(a)|=3,|vec(b)|=4 and |vec( c )|=5 . Each vector is the perpendicular to the sum of remaining two vectors. Find |vec(a)+vec(b)+vec( c )| .

vec(a) and vec(b) are any two vectors. Prove that |vec(a)+vec(b)|le|vec(a)|+|vec(b)|

Let vec(a),vec(b) and vec( c ) be unit vectors such that vec(a).vec(b)=vec(a).vec( c )=0 and the angle between vec(b) and vec( c ) is (pi)/(6) . Prove that vec(a)=+-2(vec(b)xx vec( c )) .

Let vec(X),vec(Y) and vec(Z) be three vectors such that |vec(X)|=|vec(Y)|=|vec(Z)|=sqrt(2) . The angle between vec(X),vec(Y) and vec(Z) with each other 60^(@) . vec(X)xx(vec(Y)xx vec(Z))=vec(a),vec(Y)xx(vec(Z)xx vec(X))=vec(b) and vec(X)xx vec(Y)=vec( C ) Vector vec(X) = ............... .

Let vec(X),vec(Y) and vec(Z) be three vectors such that |vec(X)|=|vec(Y)|=|vec(Z)|=sqrt(2) . The angle between vec(X),vec(Y) and vec(Z) with each other 60^(@) . vec(X)xx(vec(Y)xx vec(Z))=vec(a),vec(Y)xx(vec(Z)xx vec(X))=vec(b) and vec(X)xx vec(Y)=vec( C ) Vector vec(Y) = ............... .

Let vec(X),vec(Y) and vec(Z) be three vectors such that |vec(X)|=|vec(Y)|=|vec(Z)|=sqrt(2) . The angle between vec(X),vec(Y) and vec(Z) with each other 60^(@) . vec(X)xx(vec(Y)xx vec(Z))=vec(a),vec(Y)xx(vec(Z)xx vec(X))=vec(b) and vec(X)xx vec(Y)=vec( C ) Vector vec(Z) = ............. .

Let vec(a),vec(b) and vec( c ) be three unit vectors such that vec(a),+vec(b)+vec( c )=vec(0) . If lambda=vec(a)*vec(b)+vec(b)*vec( c )+vec( c )*vec(a) and vec(d)=vec(a)xx vec(b)+vec(b)xx vec( c )+vec( c )xx vec(a) then the ordered pair (lambda, vec(d)) is equal to :

Let vec(A), vec(B) and vec(C) , be unit vectors. Suppose that vec(A).vec(B)=vec(A).vec(C)=0 and the angle between vec(B) and vec(C) is pi/6 then

If vec(a)+vec(b)+vec( c )=0 and |vec(a)|=6,|vec(b)|=5,|vec( c )|=7 then find the angle between the vectors vec(b) and vec( c ) .