If vectors ` vec aa n d vec b` are two adjacent sides of a parallelogram, then the vector respresenting the altitude of the parallelogram which is the perpendicular to `a` is ` vec b+( vec bxx vec a)/(| vec a|^2)` b. `( vec adot vec b)/(| vec b|^2)` c. ` vec b-( vec bdot vec a)/(| vec a|^2)` d. `( vec axx( vec bxx vec a))/(| vec b|^2)`

The vector component of vec b perpendicular to vec a is ( vec bdot vec c) vec a b. ( vec axx( vec bxx vec a))/(| vec a|^2) c. vec axx( vec bxx vec a) d. none of these

The orthogonal projection of vec a on vec b is (( vec adot vec b) vec a)/(|"a"|^2) b. (( vec adot vec b) vec b)/(| vec b|^2) c. vec a/(| vec a|) d. vec b/(| vec b|)

Show that ( vec axx vec b)^2=| vec a|^2| vec b|^2-( vec adot vec b)^2=| [vec a.vec a, vec a.vec b],[ vec a.vec b, vec b.vec b]|

For any two vectors vec aa n d vec b , prove that | vec a+ vec b|lt=| vec a|+| vec b| (ii) | vec a- vec b|lt=| vec a|+| vec b| (iii) | vec a- vec b|geq| vec a|-| vec b|

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

If | vec axx vec b|^2=( vec adot vec b)^2=144\ a n d\ | vec a|=4 , find vec bdot

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))

For any two vectors vec a and vec b, prove that ((vec a) / (| vec a | ^ (2)) - (vec b) / (| vec b | ^ (2))) ^ (2) = ((vec a-vec b) / (| vec a || vec b |)) ^ (2)

If vec a_|_ vec b , then vector vec v in terms of vec aa n d vec b satisfying the equation s vec vdot vec a=0a n d vec vdot vec b=1a n d[ vec v vec a vec b]=1 is vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^2) b. vec b/(| vec b|^)+( vec axx vec b)/(| vec axx vec b|^2) c. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^) d. none of these

If | vec a|=10 ,\ | vec b|=2\ a n d\ | vec axx vec b|=16 find vec adot vec bdot