If vectors `b ,ca n dd` are not coplanar, then prove that vector `( vec axx vec b)xx( vec cxx vec d)+( vec axx vec c)xx( vec d xx vec b)+( vec axx vec d)xx( vec bxx vec c)` is parallel to ` vec adot`

For any four vectors, prove that ( vec bxx vec c)dot( vec axx vec d)+( vec cxx vec a)dot( vec bxx vec d)+( vec axx vec b)dot( vec cxx vec d)=0.

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

Prove that vec a xx (vec b + vec c) + vec b xx(vec a + vec c)+ vec c xx(vec a + vec b) = vec 0

If vec a , vec ba n d vec c are three non coplanar vectors, then prove that vec d=( vec adot vec d)/([ vec a vec b vec c])( vec bxx vec c)+( vec bdot vec d)/([ vec a vec b vec c])( vec cxx vec a)+( vec cdot vec d)/([ vec a vec b vec c])( vec axx vec b)

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

Prove that (vec(a). (vec(b) xx vec(c)) vec(a) = (vec(a) xx vec(b)) xx (vec(a) xx (c)) .

Let the pairs a , ba n dc ,d each determine a plane. Then the planes are parallel if ( vec axx vec c)xx( vec bxx vec d)= vec0 b. ( vec axx vec c)dot( vec bxx vec d)= vec0 c. ( vec axx vec b)xx( vec cxx vec d)= vec0 d. ( vec axx vec b)dot( vec cxx vec d)= vec0

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=0

If vec a+2 vec b+3 vec c=0,t h e n vec axx vec b+ vec bxx vec c+ vec cxx vec a= 2( vec axx vec b) b. 6( vec bxx vec c) c. 3( vec cxx vec a) d. vec0