` vec axx( vec bxx vec c)` , ` vec bxx( vec cxx vec a)` and ` vec cxx( vec axx vec b)` are: linearly dependent (b) coplanar vector parallel vectors (d) non coplanar vectors

If the vectors vec a+vec b+vec c,vec a+lambdavec b+2vec c,-vec a+vec b+vec c are linearly dependent then lambda

36. If vec a, vec b, vec c and vec d are unit vectors such that (vec a xx vec b) .vec c xx vec d = 1 and vec a.vec c = 1/2 then a) vec a, vec b and vec c are non-coplanar b) vec b, vec c, vec d are non -coplanar c) vec b, vecd are non parallel d) vec a, vec d are parallel and vec b, vec c are parallel

Show that the vectors 2vec a-vec b+3vec c,vec a+vec b-2vec c and vec a+vec b-3vec c are non-coplanar vectors (where vec a,vec b,vec c are non-coplanar vectors)

(vec a xxvec b)xx(vec b xxvec c)=vec b, where vec a,vec b, and vec c are nonzero vectors,then vec a,vec b, and vec c can be coplanar vec a,vec b, and vec c must be coplanar vec a,vec b, and vec c cannot be coplanar none of these

Solve the following equation for the vector vec p; vec p xx vec a+(vec p. vec b)vec c=vec b xx vec c where vec a ,vec b,vec c are non zero non coplanar vectors and vec a is neither perpendicular to vec b non to vec c hence show that (vec p xx vec a+([vec a vec b vec c])/(vec a*vec c) vec c) is perpendicular vec b-vec c.

Let vec a,vec b and vec c, be non-zero non-coplanar vectors. Prove that: vec a-2vec b+3vec c,-2vec a+3vec b-4vec c and vec c-3vec b+5vec c are coplanar vectors. 2vec a-vec b+3vec c,vec a+vec b-2vec c and vec a+vec b-3vec c are non-coplanar vectors.

If a ,ba n dc are non-cop0lanar vector, then that prove |( vec adot vec d)( vec bxx vec c)+( vec bdot vec d)( vec cxx vec a)+( vecc dot vec d)( vec axx vec b)| is independent of d ,w h e r ee is a unit vector.

If vec a is a non-zero vector and vec a * vec b = vec a * vec c, vec a xxvec b = vec a xxvec c, then

If vec a xxvec b=vec b xxvec c!=0, where vec a,vec b and vec c are coplanar vectors,then for some scalar k

If vec a and vec b are orthogonal unit vectors, then for a vector vec r noncoplanar with vec a and vec b , vector rxxa is equal to a. [ vec r vec a vec b] vec b-( vec r. vec b)( vec bxx vec a) b. [ vec r vec a vec b]( vec a+ vec b) c. [ vec r vec a vec b] vec a-( vec r. vec a) vec axx vec b d. none of these