For any two vectors ` vec ua n d vec v` prove that `( vec u . vec v)^2+| vec uxx vec v|^2=| vec u|^2| vec v|^2`

For any two vectors vec a and vec b , prove that | vec a xx vec b|^(2) = |vec a|^(2)|vec b|^(2) - (vec a . vecb)^(2) = [[veca.veca veca .vecb], [veca.vecb vec b.vecb]]

For any two vectors veca and vec b show that |vec a. vec b| le |vec a||vec b| .

For any three vectors veca, vec b, vec c prove that (vec a + vec b)+ vec c = vec a + (vec b + vec c)

If vec a , vec b , vec c ,a n d vec d are four non-coplanar unit vector such that vec d make equal angles with all the three vectors vec a , vec ba n d vec c , then prove that [ vec d vec a vec b]=[ vec d vec c vec b]=[ vec d vec c vec a]dot

For any three vectors vec a, vec b , vec c , show that vec a xx (vec b + vec c) + vec b xx (vec c + vec a) + vec c xx (vec a + vec b) = 0

vec aa n d vec b are two non-collinear unit vector, and vec u= vec a-( vec adot vec b) vec ba n d vec v= vec axx vec bdot Then | vec v| is | vec u| b. | vec u|+| vec udot vec b| c. | vec u|+| vec udot vec a| d. none of these

Let vec a , vec b ,a n d vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a]=[ vec a vec b vec c]^2dot

If vec aa n d vec b are two vectors and angle between them is theta, then | vec axx vec b|^2+( vec adot vec b)^2=| vec a|^2| vec b|^2 | vec axx vec b|=( vec adot vec b),iftheta=pi//4 vec axx vec b=( vec adot vec b) hat n ,(w h e r e hat n is unit vector, ) if theta=pi//4 ( vec axx vec b)dot( vec a+ vec b)=0

Show that for any three vectors veca , vec b and vec c [ vec a + vec b, vecb + vec c , vec c + vec a ] =2[vec a , vec b , vecc] .

If vec u , vec va n d vec w are three non-cop0lanar vectors, then prove that ( vec u+ vec v- vec w)dot( vec u- vec v)xx( vec v- vec w)= vec udot vec vdotxx vec w