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

If vec axx vec b= vec axx vec c , vec a!= vec0a n d vec b!= vec c , show that vec b= vec c+t vec a for some scalar tdot

If vec axx vec b= vec cxx vec da n d vec axx vec c= vec bxx vec d , then show that vec a- vec d , is paralelto vec b- vec c

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

If vec r. vec a=0, vec r. vec b=1 \ and \ [[ vec r ,vec a, vec b]]=1, vec adot vec b!=0,( vec adot vec b)^2-| vec a|^2| vec b|^2=-1, then find vec r in terms of vec a \ and \ vec b .

If vec a= vec p+ vec q , vec pxx vec b=0a n d vec qdot vec b=0, then prove that ( vec bxx( vec axx vec b))/( vec bdot vec b)= vec qdot

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

The condition for equations vec rxx vec a= vec ba n d vec rxx vec c= vec d to be consistent is vec bdot vec c= vec adot vec d b. vec adot vec b= vec c dot vec d c. vec bdot vec c+ vec adot vec d=0 d. vec adot vec b+ vec c dot vec d=0

[( 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 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| .