For any two vectors ` vec ua n d vec v` prove that `( vec udot vec v)^2+| vec uxx vec v|^2=| vec u|^2| vec v|^2a n d` `( vec1+| vec u|^2)( vec1+| vec v|^2)=(1- vec udot vec v)^2+| vec u+ vec v+( vec uxx vec v)|^2`

For any two vectors vec u and vec v prove that (vec udot v)^(2)+|vec u xxvec v|^(2)=|vec u|^(2)|vec v|^(2)

For any two vectors vec a and vec b ,prove that (vec a xxvec b)^(2)=|vec a|^(2)|vec b|^(2)-(vec a*vec b)^(2)

For any to vectors vec A and vec B , prove that |vec A xx vec B|^2 = A^2 B^2 - ( vec A. vec B)^2 .

For any two vectors vec a and vec b, prove that ((vec a) / (| vec a | ^ (2)) - (vec b) / (| vec b | ^ (2))) ^ (2) = ((vec a-vec b) / (| vec a || vec b |)) ^ (2)

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

For any three vectors vec a,vec b,vec c, prove that |vec a+vec b+vec c|^(2)=|vec a|^(2)+|vec b|^(2)+|vec c|^(2)+2(vec adot b+vec bvec c+vec c+vec a)

Let vec u , vec va n d vec w be vectors such that vec u+ vec v+ vec w=0. If | vec u|=3,| vec v|=4a n d| vec w|=5, then vec udot vec v+ vec vdot vec w+ vec wdot vec u is 47 b. -25 c. 0 d. 25

Let vec u ,\ vec v\ a n d\ vec w be vector such vec u+ vec v+ vec w=0.\ if | vec u|=3,\ | vec v|=4\ a n d\ | vec w|=5, then find vec udot vec vdot+ vec vdot vec w+ vec wdot vec udot

If non-zero vectors vec aa n d vec b are equally inclined to coplanar vector vec c ,t h e n vec c can be a. (| vec a|)/(| vec a|+2| vec b|)a+(| vec b|)/(| vec a|+| vec b|) vec b b. (| vec b|)/(| vec a|+| vec b|)a+(| vec a|)/(| vec a|+| vec b|) vec b c. (| vec a|)/(| vec a|+2| vec b|)a+(| vec b|)/(| vec a|+2| vec b|) vec b d. (| vec b|)/(2| vec a|+| vec b|)a+(| vec a|)/(2| vec a|+| vec b|) vec b

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)