Let ` vec r` be a non-zero vector satisfying ` vec rdot vec a= vec rdot vec b= vec rdot vec c=0` for given non-zero vectors ` vec a , vec ba n d vec cdot` Statement 1: `[ vec a- vec b vec b- vec c vec c- vec a]=0` Statement 2: `[ vec a vec b vec c]=0`

Let vec r be a non-zero vector satisfying vec r dot vec a= vec rdot vec b= vec rdot vec c=0 for given non-zero vectors vec a , vec b and vec c dot Statement 1: [ vec a- vec b vec b- vec c vec c- vec a]=0 Statement 2: [ vec a vec b vec c]=0

Let vec r be a non-zero vector satisfying vec r dot vec a= vec rdot vec b= vec rdot vec c=0 for given non-zero vectors vec a , vec b and vec c dot Statement 1: [ vec a- vec b vec b- vec c vec c- vec a]=0 Statement 2: [ vec a vec b vec c]=0

Let vec r be a non-zero vector satisfying vec r . vec a= vec r . vec b= vec r . vec c=0 for given non-zero vectors vec a , vec ba n d vec cdot Statement 1: [ vec a- vec b vec b- vec c vec c- vec a]=0 Statement 2: [ vec a vec b vec c]=0

Let vec r be a non-zero vector satisfying vec r*vec a=vec r*vec b=vec r*vec c=0 for given non- zero vectors vec a,vec b and vec c. statement 1:[vec a-vec bvec b-vec cvec c-vec a]=0 statement 2[vec avec bvec c]=0

If vec rdot vec a= vec rdot vec b= vec rdot vec c=0,w h e r e vec a , vec b ,a n d vec c are non-coplanar, then a. vec r_|_( vec cxx vec a) b. vec r_|_( vec axx vec b) c. vec r_|_( vec bxx vec c) d. vec r= vec0

If vec rdot vec a= vec rdot vec b= vec rdot vec c=0,w h e r e vec a , vec b ,a n d vec c are non-coplanar, then vec r_|_( vec cxx vec a) b. vec r_|_( vec axx vec b) c. vec r_|_( vec bxx vec c) d. vec r= vec0

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 r* vec a =0 = vec r* vec b =0 and also vec r* vec c =0 for some non-zero vector vec r , then the value of vec a*(vec b xx vec c) is........

If vec a,vec b and vec c are three non-zero vectors,prove that [vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

If vec a , vec b , vec c are three given non-coplanar vectors and any arbitrary vector vec r in space, where Delta1=| vec rdot vec a vec bdot vec a vec cdot vec a vec rdot vec b vec bdot vec b vec cdot vec b vec rdot vec c vec bdot vec c vec cdot vec c| , Delta2=| vec adot vec a vec rdot vec a vec cdot vec a vec adot vec b vec rdot vec b vec cdot vec b vec adot vec c vec rdot vec c vec cdot vec c| Delta3=| vec adot vec a vec bdot vec a vec rdot vec a vec adot vec b vec bdot vec b vec rdot vec b vec adot vec c vec bdot vec c vec rdot vec c| , Delta =| vec adot vec a vec bdot vec a vec cdot vec a vec adot vec b vec bdot vec b vec cdot vec b vec adot vec c vec bdot vec c vec cdot vec c| , then prove that vec r=(Delta1)/ Deltavec a+(Delta2)/Delta vec b+(Delta3)/Delta vec c .