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 are three vectors such that vec a+vec b+vec c=vec 0, then prove that vec a xxvec b=vec b xxvec c=vec c xxvec a

If vec a + vec b + vec c = 0, prove that (vec a xx vec b) = (vec b xx vec c) = (vec c xx vec a)

If vec(a),vec(b),vec(c) are three non-coplanar unit vector such that [vec(a),vec(b),vec(c)]=3 then [ vec(a) times vec(b), vec(b) times vec (c),vec(c) times vec(a) ] equals

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) .

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) vec(b) vec(c)]=4 then [vec(a)times vec(b) vec(b)times vec(c)vec(c) times vec(a)] =

If vec(b) and vec(c) are two non-collinear vectors such that vec(a) || (vec(b) xx vec(c)) , then (vec(a) xx vec(b)).(vec(a) xx vec(c)) is equal to

If vec(a), vec(b) and vec(c ) are mutually perpendicular unit vectors and vec(a)xx vec(b)=vec(c ) , show that vec(b)=vec(c )xx vec(a) and vec(a)=vec(b)xx vec(c ) .

If vec a,vec b,vec c are three vectors such that vec avec b=vec adot c then show that vec a=0 or ,vec b=c or vec a perp(vec b-vec c)

If vec a, vec b, vec c are three vectors such that | vec b | = | vec c | then {(vec a + vec b) xx (vec a + vec c)} xx {(vec b xxvec c)} * (vec b + vec c) =