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`

Which of the following expressions are meaningful? vec u*(vec v xxvec w) b.(vec u*vec v)*vec w c.(vec u*vec v)*vec w d.vec u xx(vec v.vec w)

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

Let vec a , vec ba n d vec c be three non-coplanar vectors and vec p , vec qa n d vec r the vectors defined by the relation vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c])a n d vec r=( vec axx vec b)/([ vec a vec b vec c])dot Then the value of the expression ( vec a+ vec b)dot vec p+( vec b+ vec c)dot vec q+( vec c+ vec a)dot vec r is a. 0 b. 1 c. 2 d. 3

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? vec x=( vec bxx vec c+ vec a+( vec cdot vec a) vec c)/(1+ vec cdot vec c) b. vec x=( vec cxx vec b+ vec b+( vec cdot vec a) vec c)/(1+ vec cdot vec c) c. vec y=( vec axx vec c+ vec b+( vec cdot vec b) vec c)/(1+ vec cdot vec c) d. none of these

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=odot

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

For any three vectors vec a, vec b, vec c, (vec a-vec b) * (vec b-vec c) xx (vec c-vec a) is equal to

If vec a , vec ba n d vec c are three non coplanar vectors, then prove that vec d=( vec adot vec d)/([ vec a vec b vec c])( vec bxx vec c)+( vec bdot vec d)/([ vec a vec b vec c])( vec cxx vec a)+( vec cdot vec d)/([ vec a vec b vec c])( vec axx vec b)

Let vec u and vec v be unit vectors such that vec u xxvec v+vec u=vec w and vec w xxvec u=vec v. Find the value of [vec uvec vvec w]

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)