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

For three vectors vec u,vec v and vec w which of the following expressions is not equal to any of the remaining three ? a.vec uvec v xxvec w b.(vec v xxvec w)vec u c.vec vvec u xxvec w d.(vec u xxvec v)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? 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

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

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 cdot vec d c. vec bdot vec c+ vec adot vec d=0 d. vec adot vec b+ vec cdot vec d=0

Let vec u ,\ vec v\ a n d\ vec w be vector such vec u+ vec v+ vec w=0.\ if | vec u|=3,\ | vec v|=4\ a n d\ | vec w|=5, then find vec udot vec vdot+ vec vdot vec w+ vec wdot vec udot

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]

Given that vec a , vec b , vec p , vec q are four vectors such that vec a+ vec b=mu vec p , vec b*vec q=0a n d|vec b|^2=1,w h e r emu is a scalar. Then |( vec adot vec q) vec p-( vec pdot vec q) vec a| is equal to a.2| vec pdot vec q| b. (1//2)| vec pdot vec q| c. | vec pxx vec q| d. | vec pdot vec q|

The vectors vec a and vec b are not perpendicular and vec c and vec d are two vectors satisfying : vec b""xxvec c""= vec b"" xxvec d"",vec a * vec d=0 . Then the vector vec d is equal to : (1) vec b-(( vec bdot vec c)/( vec adot vec d)) vec c (2) vec c+(( vec adot vec c)/( vec adot vec b)) vec b (3) vec b+(( vec bdot vec c)/( vec adot vec b)) vec c (4) vec c-(( vec adot vec c)/( vec adot vec b)) vec b

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)

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]