Let` vec r=( vec axx vec b)sinx+( vec bxx vec c)cosy+2( vec cxx vec a),w h e r e vec a , vec ba n d vec c` are there non-coplanar vectors. It is given that ` vec r` is perpendicular to ` vec a+ vec b+ vec c` , the minimum value of `x^2+y^2` is equal to (A)`pi^2` (B) `(pi^2)/4` (C)`(5pi^2)/4` (D) none of these``

If vec axx vec b= vec bxx vec c!=0,w h e r e vec a , vec b ,a n d vec c are coplanar vectors, then for some scalar k prove that vec a+ vec c=k vec bdot

The scalars la n dm such that l vec a+m vec b= vec c ,w h e r e vec a , vec ba n d vec c are given vectors, are equal to

If vec rdot vec a= vec rdot vec b= vec rdot vec c=0,w h e r e vec a , vec b ,a n d vec c are non-coplanar, then a. vec r_|_( vec cxx vec a) b. vec r_|_( vec axx vec b) c. vec r_|_( vec bxx vec c) d. vec r= vec0

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

Let vec r be a unit vector satisfying vec rxx vec a= vec b ,w h e r e| vec a|=sqrt3a n d| vec b|=sqrt2. Then

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

If vec axx vec b= vec cxx vec da n d vec axx vec c= vec bxx vec d , then show that vec a- vec d , is paralelto vec b- vec c

vec axx( vec bxx vec c) , vec bxx( vec cxx vec a) and vec cxx( vec axx vec b) are: linearly dependent (b) coplanar vector (c) parallel vectors (d) non coplanar vectors

Let vec a , vec b , a n d vec c be three non-coplanar vectors and vec d be a non-zero vector, which is perpendicular to ( vec a+ vec b+ vec c)dot Now vec d=( vec axx vec b)sinx+( vec bxx vec c)cosy+2( vec cxx vec a)dotT h e n a. ( vecd dot( vec a+ vec c))/([ vec a vec b vec c])=2 b. ( vecd dot( vec a+ vec c))/([ vec a vec b vec c])=-2 c. minimum value of x^2+y^2 is pi^2//4 d. minimum value of x^2+y^2 is 5pi^2//4