If `vec r.vec a=vec r.vec b=vec r.vec c=0` where a, b, c are non-coplanar, then

vec r*vec a=vec r*vec b=vec r*vec c=0, where vec a,vec b, and vec c are non-coplanar,then vec r perp(vec c xxvec a)bvec r perp(vec a xxvec b) c.vec r perp(vec b xxvec c) d.vec r=vec 0

If vec r . vec a= vec r . vec b= vec r . vec c=0,w h e r e vec a , vec b ,and 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 r* vec a =0 = vec r* vec b ,where vec a and vec b are non-coplanar vectors then

Let vec a xx vec b,vec b xx vec c,vec c xx vec a are non coplanar vectors and [[vec a,vec b,vec c]]=1.vec r is a vector such that vec r.vec a=vec r.vec b=vec r.vec c=2, then area of triangle whose vertices are vec a,vec b and vec c is (A) |vecr|/2 (2) 2|vecr| (C) |vecr|/4 (D) 4|vecr|

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

vec a,vec b,vec c are the three coplanar vectors and if vec r*vec a=vec r*vec b=vec r*vec c=0 then prove that vec r is a zero vector

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

If vec r . vec a= vec r . vec b= vec rdot vec c=1/2 or some nonzero vector vec r , then the area of the triangle whose vertices are A( vec a),B( vec b)a n dC( vec c)i s( vec a , vec b , vec c are non-coplanar ) a. |[ vec a vec b vec c]| b. | vec r| c. |[ vec a vec b vec c] vec r| d. none of these