` 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

If vec aa n d vec b are two vectors, then prove that ( vec axx vec b)^2=| vec adot vec a vec adot vec b vec bdot vec a vec bdot vec b| .

If vec a ,a n d vec b be two non-collinear unit vector such that vec axx( vec axx vec b)=1/2 vec b , then find the angle between vec a ,a n d vec bdot

Find | vec a|a n d| vec b|,if( vec a+ vec b)dot( vec a- vec b) = 8 , | vec a|=8| vec b|dot

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

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|=0

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)

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

Vectors vec a and vec b are non-collinear. Find for what value of n vectors vec c=(n-2) vec a+ vec b and vec d=(2n+1) vec a- vec b are collinear?

If vec a and vec b are orthogonal unit vectors, then for a vector vec r noncoplanar with vec a and vec b , vector rxxa 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

If vec ba n d vec c are two-noncollinear vectors such that vec a||( vec bxx vec c), then prove that ( vec axx vec b) . ( vec axx vec c) is equal to | vec a|^2( vec bdot vec c)dot