`vec a times(vec b timesvec c)` is equal to : (A) `(vec a*vec b)vec c-(vec a*vec c)vec b) (B)(vec a*vec b)vec a)-(vec a*vec b)vec c` (C) `(vec a*vec c)vec b-(vec a*vec b)vec c` (D) `(vec a*vec b)vec c-(vec a*vec c)vec b`

The vectors vec a and vec b are not perpendicular and vec c and vec d are two vectors satisfying : vec b""xxvec c""= vec b"" xxvec d"",vec a * vec d=0 . Then the vector vec d is equal to : (1) vec b-(( vec bdot vec c)/( vec adot vec d)) vec c (2) vec c+(( vec adot vec c)/( vec adot vec b)) vec b (3) vec b+(( vec bdot vec c)/( vec adot vec b)) vec c (4) vec c-(( vec adot vec c)/( vec adot vec b)) vec b

The length of the perpendicular form the origin to the plane passing through the point a and containing the line vec r= vec b+lambda vec c is a. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c+ vec cxx vec a|) b. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c|) c. ([ vec a vec b vec c])/(| vec bxx vec c+ vec cxx vec a|) d. ([ vec a vec b vec c])/(| vec cxx vec a+ vec axx vec b|)

( 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]

If [ vec a vec b vec c]=2, then find the value of [( vec a+2 vec b- vec c)( vec a- vec b)( vec a- vec b- vec c)]dot

( 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]

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)

If vec axx( vec bxx vec c) is perpendicular to ( vec axx vec b)xx vec c , we may have a. ( vec a. vec c)| vec b|^2=( vec a. vec b)( vec b.vec c)( vec c.vec a) b. vec adot vec b=0 c. vec adot vec c=0 d. vec bdot vec c=0

If vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero vector and |( vec d * vec c)( vec axx vec b)+( vec d* vec a)( vec bxx vec c)+( vec d*vec b)( vec cxx vec a)|=0, then a. | vec a|=| vec b|=| vec c| b. | vec a|+| vec b|+| vec c|=|d| c. vec a , vec b ,a n d vec c are coplanar d. none of these

If vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero vector and |( vec d * vec c)( vec axx vec b)+( vec d* vec a)( vec bxx vec c)+( vec d*vec b)( vec cxx vec a)|=0, then a. | vec a|=| vec b|=| vec c| b. | vec a|+| vec b|+| vec c|=|d| c. vec a , vec b ,a n d vec c are coplanar d. none of these

If vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero vector and |( vec d * vec c)( vec axx vec b)+( vec d* vec a)( vec bxx vec c)+( vec d*vec b)( vec cxx vec a)|=0, then a. | vec a|=| vec b|=| vec c| b. | vec a|+| vec b|+| vec c|=|d| c. vec a , vec b ,a n d vec c are coplanar d. none of these