If ` vec a , vec ba n d vec c` are unit vectors satisfying `| vec a- vec b|^2+| vec b- vec c|^2+| vec c- vec a|^2=9,` then `|2 vec a+5 vec b+5 vec c|` is.

If vec a , vec b , vec c are unit vector, prove that | vec a- vec b|^2+| vec b- vec c|^2+| vec c- vec a|^2lt=9.

If vec a , vec b , vec c are three unit vectors such that vecaxx vec b= vec c , vec bxx vec c= vec a, vec cxx vec a= vec b . Show that vec a , vec b , vec c from an orthonormal right handed triad of unit vectors.

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

If vec a , vec ba n d vec c are unit coplanar vectors, then the scalar triple product [2 vec a- vec b2 vec b- vec c2 vec c- vec a] is 0 b. 1 c. -sqrt(3) d. sqrt(3)

Let vec a , vec b ,and 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]^2

Prove that [[ vec a+ vec b, vec b+ vec c, vec c+ vec a]]=2[ [vec a, vec b, vec c]]dot

If vec a , vec b , vec c are unit vectors such that vec a+ vec b+ vec c= vec0, then write the value of vec a . vec b+ vec b . vec c+ vec c . vec a

If vec a ,\ vec b ,\ vec c are unit vectors such that vec a+ vec b+ vec c= vec0 find the value of vec adot vec b+ vec bdot vec c+ vec cdot vec adot'

If vec a ,\ vec b ,\ vec c are three unit vecrtors such that vec axx vec b= vec c ,\ vec bxx vec c= vec a ,\ vec cxx vec a= vec b Show that vec a ,\ vec b ,\ vec c form an orthonormal right handed triad of unit vectors.

[( 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]