If ` vec a` is perpendicular to ` vec b` and ` vec r` is non-zero vector such that `p vec r+( vec rdot vec a) vec b= vec c ,` then ` vec r=` ` vec c/p-(( vec adot vec c) vec b)/(p^2)` (b) ` vec a/p-(( vec cdot vec b) vec a)/(p^2)` ` vec a/p-(( vec adot vec b) vec c)/(p^2)` (d) ` vec c/(p^2)-(( vec adot vec c) vec b)/p`

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|)

If vec a is a non-zero vector and vec a * vec b = vec a * vec c, vec a xxvec b = vec a xxvec c, then

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

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)

If vec a, vec b and vec c are non coplaner vectors such that vec b xxvec c = vec a, vec c xxvec a = vec b and vec a xxvec b = vec c then | vec a + vec b + vec c | =

If vec a , vec b and vec c are three non-zero, non coplanar vector vec b_1= vec b-( vec bdot vec a)/(| vec a|^2) vec a , vec c_1= vec c-( vec cdot vec a)/(| vec a|^2) vec a+( vec bdot vec c)/(| vec c|^2) vec b_1 , , c_2= vec c-( vec cdot vec a)/(| vec a|^2) vec a-( vec bdot vec c)/(| vec b_1|^2) , b_1, vec c_3= vec c-( vec cdot vec a)/(| vec c|^2) vec a+( vec bdot vec c)/(| vec c|^2) vec b_1 , vec c_4= vec c-( vec cdot vec a)/(| vec c|^2) vec a=( vec bdot vec c)/(| vec b|^2) vec b_1 then the set of orthogonal vectors is ( vec a , vec b_1, vec c_3) b. ( vec a , vec b_1, vec c_2) c. ( vec a , vec b_1, vec c_1) d. ( vec a , vec b_2, vec c_2)

[[vec a + vec b-vec c, vec b + vec c-vec a, vec c + vec a-vec b is equal to

If vec r=3vec p+4vec q and 2vec r=vec p-3vec q then

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=mvec b+vec c. The scalar m is (vec c*vec b-vec a*vec c)/(a^(2)) (vec c*vec a-vec b*vec c)/(c^(2)) (vec a*vec b-vec b*vec c)/(b^(2)) (vec a-vec c)/(vec b)