If ` vec aa n d vec b` are two given vectors and `k` is any scalar, then find the vector ` vec r` satisfying ` vec rxx vec a+k vec r= vec bdot`

If vec b is not perpendicular to vec c ,then find the vector vec r satisfying the equyation vec r xxvec b=vec a xxvec b and vec r*vec c=0

If vec r*hat i=vec r*hat j=vec r*hat k and |vec r|=3, then find the vector vec r .

If vec a and vec b are two unit vectors such that vec a+vec b is also a unit vector,then find the angle between vec a and vec b.

If vec a and vec b are two unit vectors such that vec a+vec b is also a unit vector then find the angle between vec a and vec b

For any two vectors vec a\ a n d\ vec b , fin d\ ( vec axx vec b). vecbdot

If vec a and vec b are two vectors such that |vec a+vec b|=|vec a|, then prove that vector 2vec a+vec b is perpendicular to vector vec b

Let vec a and vec b be two non-zero perpendicular vectors.A vecrtor vec r satisfying the equation vec r xxvec b=vec a can be vec b-(vec a xxvec b)/(|vec b|^(2)) b.2vec b-(vec a xxvec b)/(|vec b|^(2)) c.|vec a|vec b-(vec a xxvec b)/(|vec b|^(2))d|vec b|vec b-(vec a xxvec b)/(|vec b|^(2))

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 and vec b are orthogonal unit vectors, then for a vector vec r noncoplanar with vec a and vec b , vector rxxa 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

If vec c is a given non-zero scalar,and vec A and vec B are given non-zero vector such that vec A perp B then find vector vec X which satisfies the equation vec A.vec X and vec A xxvec X=vec B .