If ` vec a` and `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 b`.

If vec b is not perpendicular to vec c , then find the vector vec r satisfying the equyation vec rxx vec b= vec axx vec b and vec r. vec c=0.

If vec a= hat i+ hat j+ hat k ,\ vec c= hat j- hat k are given vectors, then find vector vec b satisying the equation vec axx vec b= vec c\ a n d\ vec adot vec b=3.

If vec a and vec b are two non-collinear vectors having the same initial point. What are the vectors represented by vec a+ vec b and vec a- vec b .

If vec a and vec b are two non-collinear vectors having the same initial point. What are the vectors represented by vec a+ vec b and vec a- vec b .

If vec An d vec B are two vectors and k any scalar quantity greater than zero, then prove that | vec A+ vec B|^2lt=(1+k)| vec A|^2+(1+1/k)| vec B|^2dot

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

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 c is a given non-zero scalar, and vec A and vec(B) are given non-zero vector such that vec A_|_ vecB , then find vector vec X which satisfies the equation vec Adot vec X =c and vec Axx vec X= vec Bdot

Find the angle between two vectors vec a and vec b , if | vec a xx vec b|= vec a . vec b .

If vec a , vec b are two vectors, then write the truth value of the following statements: vec a=- vec b| vec a|=| vec b| | vec a|=| vec b| vec a=+- vec b | vec a|=| vec b| vec a= vec b