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.

If vec a and vec b are unequal unit vectors such that ( vec a- vec b)xx[( vec b+ vec a)xx(2 vec a+ vec b)]= vec a+ vec b , then angle theta between vec aa n d vec b is 0 b. pi//2 c. pi//4 d. pi

If vec a and vec b are unit vectors such that ( vec a+ vec b).[(2 vec a+3 vec b)xx(3 vec a-2 vec b)]=0 , then angle between veca and vec b is

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

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

If 4 vec a+5 vec b+9 vec c=0, then ( vec axx vec b)xx[( vec bxx vec c)xx( vec cxx vec a)] is equal to a. vector perpendicular to the plane of a ,b ,c b. a scalar quantity c. vec0 d. none of these

If vec a= vec p+ vec q , vec pxx vec b=0a n d vec qdot vec b=0, then prove that ( vec bxx( vec axx vec b))/( vec bdot vec b)= vec qdot

If [ vec a vec b vec c]=2, then find the value of [( vec a+2 vec b- vec c)( vec a- vec b)( vec a- vec b- vec c)]dot

Prove that , (vec(a) - vec(b)) xx (vec(a) + vec(b)) = 2 ( vec(a) xx 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 a. 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