Prove that, for any three vectors ` vec a , vec b ,` ` vec c` `[ vec a+ vec b , vec b+ vec c , vec c+ vec a]=2[ vec a , vec b , vec c]`

Prove that [[ vec a+ vec b, vec b+ vec c, vec c+ vec a]]=2[ [vec a, vec b, vec c]]dot

For any three vectors a ,\ b ,\ c prove that [ vec a+ vec b\ vec b+ vec c\ vec c+ vec a]=2\ [ vec a\ vec b\ vec c]dot

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

For any three vectors veca , vec b , vec c show that vecaxx( vec b+ vec c)+ vec bxx( vec c+ vec a)+ vec cxx( vec a+ vec b)= vec0

For any three vectors vec a , vec b , vec c , prove that | vec a+ vec b+ vec c|^2=| vec a|^2+| vec b|^2+| vec c|^2+2( vec adot vec b+ vec bdot vec c+ vec cdot vec a)

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

For any three vectors vec a ,\ vec b ,\ vec c the expression ( vec a- vec b)dot{( vec b- vec c)xx( vec c- vec a)} equals [ vec a\ vec b\ vec c] b. "\ "2[ vec a\ vec b\ vec c]"\ " c. [ vec a\ vec b\ vec c]^2 d. none of these

Show that the vectors vec a - vec b, vec b - vec c , vec c - vec a are coplaner.

[( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)( vec cxx vec a)xx( vec axx vec b)] is equal to (where vec a , vec ba n d vec c are nonzero non-coplanar vector) [ vec a vec b vec c]^2 b. [ vec a vec b vec c]^3 c. [ vec a vec b vec c]^4 d. [ vec a vec b vec c]