If `4 vec a+5 vec b+9 vec c=0,` then `( vec axx vec b)xx[( vec bxx vec c)xx( vec cxx vec a)]` is equal to a vector perpendicular to the plane of`a ,b ,c` b. a scalar quantity c. ` vec0` d. none of these

If vec a+vec b+vec c=0 , prove that (vec a xx vec b)=(vec b xx vec c)=(vec c xx vec a)

Prove that ( vec a- vec b)dot{( vec b- vec c)xx( vec c- vec a)}=0

Prove that: ( vec a- vec b)*{( vec b- vec c)xx(vec c- vec a)}"=0

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

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

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

[( 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 a is parallel to vec bxx vec c , then ( vec axx vec b)dot( vec axx vec c) is equal to | vec a|^2( vec bdot vec c) b. | vec b|^2( vec adot vec c) c. | vec c|^2( vec adot vec b) d. none of these