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

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

For any tow vectors a\ a n d\ b show that ( vec a+ vec b) ( vec a- vec b)=0 if | vec a|=| vec b|dot

Show that ( vec axx vec b)^2=| vec a|^2| vec b|^2-( vec adot vec b)^2=| [vec a.vec a, vec a.vec b],[ vec a.vec b, vec b.vec b]|

Let vec a and vec b be unit vectors such that | vec a+ vec b|=sqrt(3) . Then find the value of (2 vec a+5 vec b).((3 vec a+ vec b+ vec axx vec b))dot

If vec a+vec b+vec c=0 , prove that (vec a xx vec b)=(vec b xx vec c)=(vec c xx vec a)

Prove that ( vec a- vec b)dot{( vec b- vec c)xx( vec c- vec a)}=0

For any two vectors vec a and vec b , show that : ( vec a+ vec b)dot( vec a- vec b)=0, when | vec a|=| vec b|dot

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

If vec a , vec b ,a n d vec c are three non-coplanar non-zero vecrtors, then prove that ( vec a . vec a) vec bxx vec c+( vec a . vec b) vec cxx vec a+( vec a . vec c) vec axx vec b=[ vec b vec c vec a] vec a

Let vec a , vec ba n d vec c be three non-coplanar vecrors and vec r be any arbitrary vector. Then ( vec axx vec b)xx( vec rxx vec c)+( vec bxx vec c)xx( vec rxx vec a)+( vec cxx vec a)xx( vec rxx vec b) is always equal to [ vec a vec b vec c] vec r b. 2[ vec a vec b vec c] vec r c. 3[ vec a vec b vec c] vec r d. none of these