If ` vec rdot vec a= vec rdot vec b= vec rdot vec c=0,w h e r e vec a , vec b ,a n d vec c` are non-coplanar, then a.` vec r_|_( vec cxx vec a)` b. ` vec r_|_( vec axx vec b)` c. ` vec r_|_( vec bxx vec c)` d. ` vec r= vec0`

If vec axx vec b= vec bxx vec c!=0,w h e r e vec a , vec b ,a n d vec c are coplanar vectors, then for some scalar k prove that vec a+ vec c=k vec bdot

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then

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

[( 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]

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

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.

Let vec r be a non-zero vector satisfying vec r dot vec a= vec rdot vec b= vec rdot vec c=0 for given non-zero vectors vec a , vec b and vec c dot Statement 1: [ vec a- vec b vec b- vec c vec c- vec a]=0 Statement 2: [ vec a vec b vec c]=0

Vectors vec Aa n d vec B satisfying the vector equation vec A+ vec B= vec a , vec Axx vec B= vec ba n d vec A*vec a=1,w h e r e vec aa n d vec b are given vectors, are a. vec A=(( vec axx vec b)- vec a)/(a^2) b. vec B=(( vec bxx vec a)+ vec a(a^2-1))/(a^2) c. vec A=(( vec axx vec b)+ vec a)/(a^2) d. vec B=(( vec bxx vec a)- vec a(a^2-1))/(a^2)

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.

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