Prove that `(vec a xx vec b)^2=vec a^2.vecb^2-(vec a. vecb)^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. vec b)^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)

Prove that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b) and interpret it geometrically.

Prove that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b) and interpret it geometrically.

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 vec a\ a n d\ vec b prove that | vec axx vec b|^2=| (veca. veca , veca. vecb),(vecb.veca ,vecb.vecb)|

For any two vectors vec a\ a n d\ vec b prove that | vec axx vec b|^2=| (veca. veca , veca. vecb),(vecb.veca ,vecb.vecb)|

Prove that ([vec a-vec b])xx(vec a+vec b)=2(vec a xxvec b) and interpret it geometrically.

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 .