` vec ba n d vec c` are unit vectors. Then for any arbitrary vector ` vec a ,((( vec axx vec b)+( vec axx vec c))xx( vec bxx vec c))dot( vec b- vec c)` is always equal to a.`| vec a|` b. `1/2| vec a|` c. `1/3| vec a|` d. none of these

vec ba n d vec c are unit vectors. Then for any arbitrary vector vec a ,((( vec axx vec b)+( vec axx vec c))xx( vec bxx vec c)).( vec b- vec c) is always equal to a. | vec a| b. 1/2| vec a| c. 1/3| vec a| d. none of these

vec b and vec c are unit vectors.Then for any arbitrary vector vec a,(((vec a xxvec b)+(vec a xxvec c))xx(vec b xxvec c))vec b-vec c is always equal to a.|vec a| b.(1)/(2)|vec a| c.(1)/(3)|vec a| d.none of these

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

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

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 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.

Let vec a , vec b ,a n d 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]^2dot

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 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 parallel to vec b- vec c