If `( vec axx vec b)xx( vec cxx vec d)dot( vec axx vec d)=0` , then which of the following may be true? ` vec a , vec b , vec ca n d vec d` are necessarily coplanar b.` vec a` lies in the plane of ` vec ca n d vec d` c. ` vec b` lies in the plane of ` vec aa n d vec d` d. ` vec c` lies in the plane of ` vec aa n d vec d`

If vec a , vec b , vec c , vec d are non-zero, non collinear vectors and if ( vec aX vec b)X( vec cX vec d)dot( vec aXvec d)=0 , then which of the following is always true. (a) vec a , vec b , vec c , vec d are necessarily coplanar (b) either vec a or vec d must lie in the plane of vec b and vec c (c) either vec b or vec c must lie in plane of vec a and vec d (d) either vec a or vec b must lie in plane of vec c and vec d

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

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d). (vec b- vec c)!=0,

[( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)( vec cxx vec a)xx( vec axx vec b)] is equal to (where vec a , vec ba n d vec c are nonzero non-coplanar vector) [ vec a vec b vec c]^2 b. [ vec a vec b vec c]^3 c. [ vec a vec b vec c]^4 d. [ vec a vec b vec c]

If ( vec axx vec b)xx( vec bxx vec c)= vec b ,w h e r e vec a , vec b ,a n d vec c are nonzero vectors, then 1. vec a , vec b ,a n d vec c can be coplanar 2. vec a , vec b ,a n d vec c must be coplanar 3. vec a , vec b ,a n d vec c cannot be coplanar 4.none of these

If vec a\ a n d\ vec b are two vectors such that | vec axx vec b|=3\ a n d\ vec adot vec b=1, find the angle between vec a\ a n d\ vec b .

If vec axx vec b= vec cxx vec d\ a n d\ vec axx vec c= vec bxx vec d ,\ show that vec a- vec d is parallel to vec b- vec c , w h e r e\ vec a!= vec d\ a n d\ vec b!= vec c

If vec aa n d vec b are two vectors such that | vec axx vec b|=2, then find the value of [ vec a vec b vec axx vec b]dot

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then

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