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.`

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

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

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

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

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

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 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 a ,\ b ,\ c are non coplanar vectors then ( vec adot( vec bxx vec c))/(( vec cxx vec a)dot vec b)+( vec bdot( vec axx vec c))/( vec cdot( vec axx vec b)) is equal to 2 b. "\ "0"\ " c. 1 d. none of these

For any four vectors, vec a , vec b , vec c and vec d prove that vec d.( vec axx( vec bxx( vec cxx vec d)))=( vec b. vec d)[ vec a \ vec c \ vec d] .

For any four vectors, vec a , vec b , vec c and vec d prove that vec d.( vec axx( vec bxx( vec cxx vec d)))=( vec b. vec d)[ vec a \ vec c \ vec d] .