For any three vectors `adotb\ a n d\ c` write the value of ` vec axx( vec b+ vec c)+ vec bxx( vec c+ vec a)+ vec cxx( vec a+ vec b)dot`

For any three vectors vec a,vec b and vec c, write the value of the following: vec a xx(vec b+vec c)+vec b xx(vec c+vec a)+vec c xx(vec a+vec b)

For any three vectors a b,c,show that vec a xx(vec b+vec c)+vec b xx(vec c+vec a)+vec c xx(vec a+vec b)=0

If the vectors vec a, vec b, vec c are coplanar, then the value of | (vec a, vec b, vec c), (vec a * vec a, vec a * vec b, vec a * vec c), (vec b * vec a, vec b * vec b, vecb * vec c) | =

If vec a,vec b, and vec c are three non-coplanar vectors,then find the value of (vec a*(vec b xxvec c))/(vec b*(vec c xxvec a))+(vec b*(vec c xxvec a))/(vec c*(vec a xxvec b))+(vec c*(vec b xxvec a))/(vec a xxvec c))

For any three non-zero vectors vec a, vec b and vec c if | (vec a xxvec b) * vec c | = | vec a || vec b || vec c | then vec a * vec b + vec b * vec c + vec c * vec a =

If vec a, vec b, vec c are unit vectors such that vec a + vec b + vec c = vec 0 find the value of vec a * vec b + vec b * vec c + vec c * vec avec a * vec b + vec b * vec c + vec c * vec a

For any two vectors vec a\ a n d\ vec b , fin d\ ( vec axx vec b). vecbdot

If vec a , vec ba n d vec c are three non coplanar vectors, then prove that vec d=( vec adot vec d)/([ vec a vec b vec c])( vec bxx vec c)+( vec bdot vec d)/([ vec a vec b vec c])( vec cxx vec a)+( vec cdot vec d)/([ vec a vec b vec c])( vec axx vec b)

Let vec a , vec ba n d vec c be three non-coplanar vectors and vec p , vec qa n d vec r the vectors defined by the relation vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c])a n d vec r=( vec axx vec b)/([ vec a vec b vec c])dot Then the value of the expression ( vec a+ vec b)dot vec p+( vec b+ vec c)dot vec q+( vec c+ vec a)dot vec r is a. 0 b. 1 c. 2 d. 3

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) =