If ` vec axx( vec bxx vec c)` is perpendicular to `( vec axx vec b)xx vec c ,` we may have `( vec adot vec c)| vec b|^2=( vec adot vec b)( vec bdot vec c)` b. ` vec adot vec b=0` c. ` vec adot vec c=0` d. ` vec bdot vec c=0`

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

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

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 b , vec c are three given non-coplanar vectors and any arbitrary vector vec r in space, where Delta1=| vec rdot vec a vec bdot vec a vec cdot vec a vec rdot vec b vec bdot vec b vec cdot vec b vec rdot vec c vec bdot vec c vec cdot vec c| , Delta2=| vec adot vec a vec rdot vec a vec cdot vec a vec adot vec b vec rdot vec b vec cdot vec b vec adot vec c vec rdot vec c vec cdot vec c| Delta3=| vec adot vec a vec bdot vec a vec rdot vec a vec adot vec b vec bdot vec b vec rdot vec b vec adot vec c vec bdot vec c vec rdot vec c| , Delta =| vec adot vec a vec bdot vec a vec cdot vec a vec adot vec b vec bdot vec b vec cdot vec b vec adot vec c vec bdot vec c vec cdot vec c| , then prove that vec r=(Delta1)/ Deltavec a+(Delta2)/Delta vec b+(Delta3)/Delta vec c .

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

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then vec b= vec c b. vec b=0 c. vec b+ vec c=0 d. none of these

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

Line vec r= vec a+lambda vec b will not meet the plane vec rdot vec n=q , if a. vec bdot vec n=0, vec adot vec n=q b. vec bdot vec n!=0, vec adot vec n!=q c. vec bdot vec n=0, vec adot vec n!=q d. vec bdot vec n!=0, vec adot vec n=q

If vec a + vec b + vec c = 0, prove that (vec a xx vec b) = (vec b xx vec c) = (vec c xx vec a)

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]|