If ` vec a , vec ba n d vec c` are three non-zero non-coplanar vectors, then find the linear relation between the following four vectors: ` vec a-2 vec b+3 vec c ,2 vec a-3 vec b+4 vec c ,3 vec a-4 vec b+5 vec c ,7 vec a-11 vec b+15 vec cdot`

If vec a,vec b, and vec c are non-zero vectors such that vec a.vec b=vec a*vec c, then find the geometrical relation between the vectors.

Show that the points with position vectors vec a-2vec b+3vec c,-2vec a+3vec b-vec c and 4vec a-7vec b+7vec c are collinear.

For any three vectors vec a;vec b;vec c find [vec a+vec b;vec b+vec c;vec c+vec a]

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 .

If vec a , vec b and vec c are three non-zero, non coplanar vector vec b_1= vec b-( vec bdot vec a)/(| vec a|^2) vec a , vec c_1= vec c-( vec cdot vec a)/(| vec a|^2) vec a+( vec bdot vec c)/(| vec c|^2) vec b_1 , , c_2= vec c-( vec cdot vec a)/(| vec a|^2) vec a-( vec bdot vec c)/(| vec b_1|^2) , b_1, vec c_3= vec c-( vec cdot vec a)/(| vec c|^2) vec a+( vec bdot vec c)/(| vec c|^2) vec b_1 , vec c_4= vec c-( vec cdot vec a)/(| vec c|^2) vec a=( vec bdot vec c)/(| vec b|^2) vec b_1 then the set of orthogonal vectors is ( vec a , vec b_1, vec c_3) b. ( vec a , vec b_1, vec c_2) c. ( vec a , vec b_1, vec c_1) d. ( vec a , vec b_2, vec c_2)

If a,b, are non coplanar vectors prove that the points having the following position vectors are collinear: vec a+vec b+vec c,4vec a+3vec b,10vec a+7vec b-2vec -

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)

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

Show that the vectors vec a-2vec b+3vec c,vec a-3vec b+5vec c and -2vec a+3vec b-4vec c are coplanar,where vec a,vec b,vec c are non-coplanar.

If a,b,c are non zero non coplanar vectors,prove that the following vectors are coplanar.5vec a+6vec b+7vec c,7vec a-8vec b+9vec c and 3vec a+20vec b+5vec c