Given `| vec a|=| vec b|=1a n d| vec a+ vec b|=sqrt(3).` If ` vec c` is a vector such that ` vec c- vec a-2 vec b=3( vec axx vec b),` then find the value of ` vec c dot vec b`

If vec a,vec b,vec c are unit vectors such that vec a+vec b+vec c=vec 0 find the value of vec a+vec b+vec bdot c+vec *vec a

If vec a,vec b and vec c be three vectors such that vec a+vec b+vec c=0,|vec a|=1,|vec c|=3,|vec b|=2, Then find the value of vec a.vec b+vec b.vec c+vec c.vec a

If vec a,vec b, and vec c are unit vectors such that vec a+vec b+vec c=0, then find 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=vec 0, 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 three vectors such that vec a+vec b+vec c=vec 0 and |vec a|=3,|b|=4,|vec c|=5 Find the value of vec a*vec b+vec b*vec c+vec c*vec a

Let vec a , vec ba n d vec c be three non-coplanar vectors and vec p , vec qa n d vec r the vectors defined by the relation vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c])a n d vec r=( vec axx vec b)/([ vec a vec b vec c])dot Then the value of the expression ( vec a+ vec b)dot vec p+( vec b+ vec c)dot vec q+( vec c+ vec a)dot vec r is a. 0 b. 1 c. 2 d. 3

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

If vec a, vec b and vec c are perpendicular to vec b + vec c, vec c + vec a, vec a + vec b respectively and if | vec a + vec b | = 6, | vec b + vec c | = 8 and | vec c + vec a | = 10 then find the value of vec a + vec b + vec c

If vec a,vec b, and vec c are three vectors such that vec a xxvec b=vec c,vec b xxvec c=vec a,vec c xxvec a=vec b then prove that |vec a|=|vec b|=|vec c|

If vec a, vec b and vec c are non coplaner vectors such that vec b xxvec c = vec a, vec c xxvec a = vec b and vec a xxvec b = vec c then | vec a + vec b + vec c | =