Show that `| vec a| vec b+| vec b| vec a` is a perpendicular to `| vec a| vec b-| vec b| vec a ,` for any two non-zero vectors ` vec aa n d vec bdot`

Let vec a , vec b , and vec c are vectors such that | vec a|=3,| vec b|=4 and | vec c|=5, and ( vec a+ vec b) is perpendicular to vec c ,( vec b+ vec c) is perpendicular to vec a and ( vec c+ vec a) is perpendicular to vec bdot Then find the value of | vec a+ vec b+ vec c| .

If vec c is perpendicular to both vec a\ a n d\ vec b , then prove that it is perpendicular to both vec a+ vec b\ a n d\ vec a- vec bdot

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

Show that vectors vec a ,\ vec b ,\ vec c are coplanar if vec a+ vec b ,\ vec b+ vec c ,\ vec c+ vec a are coplanar.

Show that the vectors vec a , vec b and vec c are coplanar if vec a+ vec b , vec b+ vec c and vec c+ vec a are coplanar.

vec rxx vec a= vec bxx vec a ; vec rxx vec b= vec axx vec b ; vec a!= vec0; vec b!= vec0; vec a!=lambda vec b ,a n d vec a is not perpendicular to vec b , then find vec r in terms of vec aa n d vec bdot

If vec a\ a n d\ vec b are two vectors such that | vec a|=| vec axx vec b|, write the angle between vec a\ a n d\ vec bdot

For any vector vec a\ a n d\ vec b prove that | vec a+ vec b|lt=| vec a|+| vec b|dot

Given that vec adot vec b= vec adot vec c , vec axx vec b= vec axx vec c and vec a is not a zero vector. Show that vec b= vec c dot