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|^2`

For any two vectors vec a and vec b prove that | vec a + vec b | <= | vec a | + | vec b |

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 two vectors vec aa n d vec b , prove that | vec a+ vec b|lt=| vec a|+| vec b| (ii) | vec a- vec b|lt=| vec a|+| vec b| (iii) | vec a- vec b|geq| vec a|-| vec b|

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 vector vec a and vec b prove that |vec a+vec b|<=|vec a|+|vec b|

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)

For any two vectors vec a\ a n d\ vec b , fin d\ ( vec axx vec b). vecbdot

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)

For any vector vec a, prove that |vec a xxhat i|^(2)+|vec a xxhat j|^(2)+|vec a xxhat k|^(2)=2|vec a|^(2)

If vec a,vec b,vec c are unit vector,prove that |vec a-vec b|^(2)+|vec b-vec c|^(2)+|vec c-vec a|^(2)<=9