The condition for equations ` vec rxx vec a= vec ba n d vec rxx vec c= vec d` to be consistent is a.` vec b . vec c= vec a . vec d` b. ` vec a . vec b= vec c .vec d` c. ` vec b . vec c+ vec a . vec d=0` d. ` vec adot vec b+ vec c .vec d=0`

Prove that [ vec a, vec b, vec c + vec d] = [ vec a, vec b, vec c] + [ vec a, vec b , vec d] .

Value of [ vec axx vec b vec axx vec c vec d] is always equal to ( vec a . vec d)[ vec a vec b vec c] b. ( vec a . vec c)[ vec a vec b vec d] c. ( vec a . vec b)[ vec a vec b vec d] d. none of these

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) b. vec adot vec b=0 c. vec adot vec c=0 d. vec bdot vec c=0

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=0

If vec a , vec ba n d vec c are non coplanar vectors and vec axx vec c is perpendicular to vec axx( vec bxx vec c), then the value of [axx( vec bxx vec c)]xx vec c is equal to a. [ vec a vec b vec c] b. 2[ vec a vec b vec c] vec b c. vec0 d. [ vec a vec b vec c] vec a

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

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d)dot (vec b- vec c)!=0,

Given that vec adot vec b= vec adot vec c , vec axx vec b= vec axx vec ca n d vec a is not a zero vector. Show that vec b= vec cdot

Prove that if the vectors vec a, vec b, vec c satisfy vec a+ vec b + vec c = vec 0 , then vec bxx vec c = vec c xx vec a = vec a xx vec b

For any three vectors vec a, vec b , vec c , show that vec a xx (vec b + vec c) + vec b xx (vec c + vec a) + vec c xx (vec a + vec b) = 0