`( vec a+2 vec b- vec c)dot{( vec a- vec b)xx( vec a- vec b- vec c)}` is equal to `[ vec a\ vec b\ vec c]` b. c. `2[ vec a\ vec b\ vec c]` d. `3[ vec a\ vec b\ vec c]`

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 a ,\ vec b ,\ vec c are three non coplanar vectors, then ( vec a+ vec b+ vec c)dot[( vec a+ vec b)xx) vec a+ vec c)] equals [ vec a\ vec b\ vec c] b. "\ "0"\ " c. 2[ vec a\ vec b\ vec c] d. -[ vec a\ vec b\ vec c]

For any three vectors vec a ,\ vec b ,\ vec c the expression ( vec a- vec b)dot{( vec b- vec c)xx( vec c- vec a)} equals [ vec a\ vec b\ vec c] b. "\ "2[ vec a\ vec b\ vec c]"\ " c. [ vec a\ vec b\ vec c]^2 d. none of these

( vec a+ vec b)dot( vec b+ vec c)xx( vec a+ vec b+ vec c)= [ vec a\ vec b\ vec c] b. "\ "0"\ " c. 2[ vec a\ vec b\ vec c] d. -[ vec a\ 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

If vec a , vec b and vec c are three non-coplanar vectors, then ( vec a+ vec b+ vec c).[( vec a+ vec b)xx( vec a+ vec c)] equals a. 0 b. [ vec a vec b vec c] c. 2[ vec a vec b vec c] d. -[ vec a vec b vec c]

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

Prove that [[ vec a+ vec b, vec b+ vec c, vec c+ vec a]]=2[ [vec a, vec b, vec c]]dot