If ` vec a , vec b , vec c ,a n d vec d` are four non-coplanar unit vector such that ` vec d` make equal angles with all the three vectors ` vec a , vec ba n d vec c` , then prove that `[ vec d vec a vec b]=[ vec d vec c vec b]=[ vec d vec c vec a]dot`

Prove that [vec a,vec b,vec c+vec d]=[vec a,vec b,vec c]+[vec a,vec b,vec d]

[vec a, vec b + vec c, vec d] = [vec a, vec b, vec d] + [vec a, vec c, vec d]

For any four vectors,vec a,vec b,vec c and vec d prove that vec d*(vec a xx(vec b xx(vec c xxvec d)))=(vec b*vec d)[vec avec cvec d]

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]

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] =>vec d is equally inclined to veca,vecb,vecc.

The vectors vec a,vec b,vec c,vec d are coplanar then

If the three vectors vec a,vec b,vec c are coplanar, prove that the vectors vec a+vec b,vec b+vec c and vec c+vec a are also 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.

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.

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