Which of the following expressions are meaningful? a. ` vec u.(vec vxx vec w)` b. `vec u. vec v. vec w` c. `( vec u vec v). vec w` d. ` vec uxx( vec v. vec w)`

Which of the following expressions are meaningful? vec u.( vec vxx vec w) b. ( vec u. vec v). vec w c. ( vec u. vec v). vec w d. vec uxx( vec v. vec w)

For three vectors vec u , vec va n d vec w which of the following expressions is not equal to any of the remaining three ? a. vec udot( vec vxx vec w) b. ( vec vxx vec w)dot vec u c. vec vdot( vec uxx vec w) d. ( vec uxx vec v)dot vec w

If vec x+ vec cxx vec y= vec aa n d vec y+ vec cxx vec x= vec b ,w h e r e vec c is a nonzero vector, then which of the following is not correct? a. vec x=( vec bxx vec c+ vec a+( vec c dot vec a) vec c)/(1+ vec c dot vec c) b. vec x=( vec cxx vec b+ vec b+( vec c dot vec a) vec c)/(1+ vec c dot vec c) c. vec y=( vec axx vec c+ vec b+( vec c dot vec b) vec c)/(1+ vec c dot vec c) d. none of these

If vec a in the plane of vectors vec b\ a n d\ vec c then which of the following is correct? [ vec a\ vec b\ vec c]=0 b. "\" [ vec a\ vec b\ vec c]=1' c. "[ vec a\ vec b\ vec c]=3" d. "[ vec b\ vec c\ vec a]=1"

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

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

Let vec u and vec v be unit vectors such that vec uxx vec v+ vec u= vec w and vec wxx vec u= vec v . Find the value of [ vec u \ vec v \ vec w] .

If vec a , vec b ,a n d vec c are three non-coplanar non-zero vecrtors, then prove that ( vec a . vec a) vec bxx vec c+( vec a . vec b) vec cxx vec a+( vec a . vec c) vec axx vec b=[ vec b vec c vec a] vec a

Let vec ua n d vec v be unit vectors such that vec uxx vec v+ vec u= vec w and vec wxx vec u= vec vdot Find the value of [ vec u vec v vec w]dot

If vec a and vec b are orthogonal unit vectors, then for a vector vec r noncoplanar with vec a and vec b , vec rxx veca is equal to a. [ vec r vec a vec b] vec b-( vec r. vec b)( vec bxx vec a) b. [ vec r vec a vec b]( vec a+ vec b) c. [ vec r vec a vec b] vec a-( vec r. vec a) vec axx vec b d. none of these