If ` vec axx vec b= vec bxx vec c!=0,w h e r e vec a , vec b ,a n d vec c` are coplanar vectors, then for some scalar `k` prove that ` vec a+ vec c=k vec bdot`

If ( vec axx vec b)xx( vec bxx vec c)= vec b ,w h e r e vec a , vec b ,a n d vec c are nonzero vectors, then (a) vec a , vec b ,a n d vec c can be coplanar (b) vec a , vec b ,a n d vec c must be coplanar (c) vec a , vec b ,a n d vec c cannot be coplanar (d)none of these

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 axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)( vec cxx vec a)xx( vec axx vec b)] is equal to (where vec a , vec ba n d vec c are nonzero non-coplanar vector) [ vec a vec b vec c]^2 b. [ vec a vec b vec c]^3 c. [ vec a vec b vec c]^4 d. [ vec a vec b vec c]

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

vec rxx vec a= vec bxx vec a ; vec rxx vec b= vec axx vec b ; vec a!= vec0; vec b!= vec0; vec a!=lambda vec b ,a n d vec a is not perpendicular to vec b , then find vec r in terms of vec aa n d vec bdot

Vectors vec Aa n d vec B satisfying the vector equation vec A+ vec B= vec a , vec Axx vec B= vec ba n d vec A*vec a=1,w h e r e vec aa n d vec b are given vectors, are a. vec A=(( vec axx vec b)- vec a)/(a^2) b. vec B=(( vec bxx vec a)+ vec a(a^2-1))/(a^2) c. vec A=(( vec axx vec b)+ vec a)/(a^2) d. vec B=(( vec bxx vec a)- vec a(a^2-1))/(a^2)

Let vec a , vec b ,a n d vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a]=[ vec a vec b vec c]^2dot

Show that the vectors vec a, vec b and vec c are coplanar if vec a + vec b, vec b + vec c, vec c+ vec a are coplanar.

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