If ` vec axx vec b= vec axx vec c , vec a!= vec0a n d vec b!= vec c` , show that ` vec b= vec c+t vec a` for some scalar `tdot`

If vec a xxvec b=vec a xxvec c,vec a!=vec 0 and vec b!=vec c show that vec b=vec c+tvec a for some scalar t

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

[vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

[vec a, vec b + vec c, vec d] = [vec a, vec b, vec d] + [vec a, vec c, vec d]

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 adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then vec b= vec c b. vec b=0 c. vec b+ vec c=0 d. none of these

If the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n vec adot vec b+ vec bdot vec c+ vec cdot vec a=0 b. vec axx vec b= vec bxx vec c= vec cxx vec a c. vec adot vec b= vec bdot vec c= vec cdot vec a d. vec axx vec b+ vec bxx vec c+ vec cxx vec a=0

If vec a xxvec b=vec c xxvec d and vec a xxvec c=vec b xxvec d then show that vec a-vec d is parallel to vec b-vec c where a!=d and b!=c

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|)

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] =>vec d is equally inclined to veca,vecb,vecc.