Let ` vec r` be a non-zero vector satisfying ` vec rdot vec a= vec rdot vec b= vec rdot vec c=0` for given non-zero vectors ` vec a , vec ba n d vec cdot` Statement 1: `[ vec a- vec b vec b- vec c vec c- vec a]=0` Statement 2: `[ vec a vec b vec c]=0`

If vec a is a non-zero vector and vec a * vec b = vec a * vec c, vec a xxvec b = vec a xxvec c, then

If vec x.vec a=0,vec x*vec b=0 and vec x*vec c=0 for some non-zero vector vec x ,then prove that [vec avec bvec c]=0

If vec a,vec b and vec c are three non-zero vectors,prove that [vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

The non-zero vectors are vec a,vec b and vec c are related by vec a=8vec b and vec c=-7vec b. Then the angle between vec a and vec c is

If vec a , vec b , vec c are three given non-coplanar vectors and any arbitrary vector vec r in space, where Delta1=| vec rdot vec a vec bdot vec a vec cdot vec a vec rdot vec b vec bdot vec b vec cdot vec b vec rdot vec c vec bdot vec c vec cdot vec c| , Delta2=| vec adot vec a vec rdot vec a vec cdot vec a vec adot vec b vec rdot vec b vec cdot vec b vec adot vec c vec rdot vec c vec cdot vec c| Delta3=| vec adot vec a vec bdot vec a vec rdot vec a vec adot vec b vec bdot vec b vec rdot vec b vec adot vec c vec bdot vec c vec rdot vec c| , Delta =| vec adot vec a vec bdot vec a vec cdot vec a vec adot vec b vec bdot vec b vec cdot vec b vec adot vec c vec bdot vec c vec cdot vec c| , then prove that vec r=(Delta1)/ Deltavec a+(Delta2)/Delta vec b+(Delta3)/Delta vec c .

If for three non zero vectors vec a,vec b and vec cvec a*vec b=vec a.vec c and vec a xxvec b=vec a xxvec c, the show that vec b=vec c .

Let vec a, vec b, vec c be three nonzero vectors such that vec a + vec b + vec c = vec 0 and lambdavec b xxvec a + vec b xxvec c + vec c xxvec a = 0 then lambda is

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then vec b= vec c b. vec b=0 c. vec b+ vec c=0 d. none of these

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

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 =