If `| vec a|=a` and `| vec b|=b ,` prove that `( vec a/(a^2)- vec b/(b^2))^2` = `(( vec a- vec b)/(a b))^2` .

If | vec a|= a\ a n d\ | vec b|=b, prove that ( vec a/(a^2)- vec b/(b^2))^2=(( vec a- vec b)/(a b))^2

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

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

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. vec b)^2

Find | vec a|a n d| vec b|,if( vec a - vec b)dot ( vec a+ vec b) =27 and | vec a|=2| vec b|dot

Prove the inequality (vec(a) * vec(b) )^(2) le |vec(a)|^(2)|vec(b)|^(2)

Find | vec a|a n d\ | vec b| , if : ( vec a+ vec b)dot'( vec a- vec b)=12\ a n d\ | vec a|=2| vec b|

Find | vec a|a n d\ | vec b| , if : ( vec a+ vec b)dot'( vec a- vec b)=13\ a n d\ | vec a|=2| vec b|

If vec a and vec b are two vectors, then prove that ( vec axx vec b)^2=|[vec a.vec a,vec a.vec b],[vec b.vec a,vec b.vec b]| .

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