If `vec(a).vec(b)=0 and vec(a) xx vec(b)=0, " prove that " vec(a)= vec(0) or vec(b)=vec(0)`.

If vec(a), vec(b), vec(c ) are three vectors such that vec(a)xx vec(b)=vec(c ), vec(b)xx vec(c )=vec(a) , prove that vec(a), vec(b), vec(c ) are mutually at right angles and |vec(b)|=1, |vec(c )|=|vec(a)| .

if vec(a) + 2vec(b) + 3vec(c ) = 0 and vec(a) xx vec(b) + vec(b) xx vec(c ) + vec(c ) xx vec(a) = lamda (vec(b) xx vec(c )) then what is the value of lamda ?

If vec(a), vec(b), vec(c ) are three vectors such that vec(a)+vec(b)+vec(c )=0 , then prove that : vec(a)xx vec(b)=vec(b)xx vec(c )=vec(c )xx vec(a) and hence, show that [vec(a)vec(b)vec(c )]=0 .

If vec(A)+vec(B)+vec(C )=0 then vec(A)xx vec(B) is

If vec(a).vec(b)xx vec(c )≠0 and vec(a')=(vec(b)xx vec(c ))/(vec(a).vec(b)xx vec(c )), vec(b')=(vec(c )xx vec(a))/(vec(a).vec(b)xx vec(c )), vec(c')=(vec(a)xx vec(b))/(vec(a).vec(b)xx vec(c )) , show that : vec(a).vec(a')+vec(b).vec(b')+vec(c ).vec(c')=3

If vec(a) , vec(b) and vec(c ) be three vectors such that vec(a) + vec(b) + vec(c )=0 and |vec(a)|=3, |vec(b)|=5,|vec(C )|=7 , find the angle between vec(a) and vec(b) .

For three non-zero vectors vec(a),\vec(b) " and"vec(c ) , prove that [(vec(a)-vec(b))\ \ (vec(b)-vec(c))\ \ (vec(c )-vec(a))]=0

If vec(a),vec(b) and vec(c ) are three vectors such that vec(a)+vec(b)+vec(c )=vec(0) and |vec(a)|=2,|vec(b)|=3 and |vec(c )|=5 , then the value of vec(a)*vec(b)+vec(b)*vec(c)+vec(c)*vec(a) is

If vec(a).vec(b)xx vec(c ) ≠ 0 and vec(a')=(vec(b)xx vec(c ))/(vec(a).vec(b)xx vec(c )), vec(b')=(vec(c )xx vec(a))/(vec(a).vec(b)xx vec(c )), vec(c')=(vec(a)xx vec(b))/(vec(a).vec(b)xx vec(c )) , show that : vec(a').(vec(b')xx vec(c'))=(1)/(vec(a).(vec(b)xx vec(c )))

If vec(a).vec(b)xx vec(c ) ≠ 0 and vec(a')=(vec(b)xx vec(c ))/(vec(a).vec(b)xx vec(c )), vec(b')=(vec(c )xx vec(a))/(vec(a).vec(b)xx vec(c )), vec(c')=(vec(a)xx vec(b))/(vec(a).vec(b)xx vec(c )) , show that : vec(a).vec(a')+vec(b). vec(b')+vec(c ). vec(c')=3 .