Let ` vec a , vec b` and `vec c` be three non-zero vectors such that ` vec a+ vec b+ vec c=0` and `lambda vec bxx vec a+ vec bxx vec c+ vec cxx vec a=0,` then find the value of `lambda`

Let vec a , vec ba n d vec c be three verctors such that vec a!=0,| vec a|=| vec c|=1,| vec b|=4 and | vec bxx vec c|=sqrt(15)dot If vec b-2 vec c=lambda vec a , then find the value of lambda

If vec a+ vec b+ vec c = vec 0 then prove that vec axx vec b= vec bxx vec c = vec cxxvec a .

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

If vec a , vec b , and vec c are three vectors such that vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b , then prove that | vec a|=| vec b|=| vec c| .

Let vec a , vec ba n d vec c be unit vectors, such that vec a+ vec b+ vec c= vec x , vec a dot vec x=1, vec b dot vec x=3/2,| vec x|=2. Then find the angle between vec c and vec x

If vec a , vec b and vec c are three non-zero vectors, no two of which are collinear, vec a+2 vec b is collinear with vec c and vec b+3 vec c is collinear with vec a , then find the value of | vec a+2 vec b+6 vec c| .

Let vec a , vec b and vec c be unit vectors such that vec a+ vec b- vec c=0. If the area of triangle formed by vectors vec a and vec b is A , then what is the value of 4A^2?

Let vec a , vec b , and vec c are vectors such that | vec a|=3,| vec b|=4 and | vec c|=5, and ( vec a+ vec b) is perpendicular to vec c ,( vec b+ vec c) is perpendicular to vec a and ( vec c+ vec a) is perpendicular to vec bdot Then find the value of | vec a+ vec b+ vec c| .

Let vec a , vec b ,a n d vec c be non-zero vectors and vec V_1= vec axx( vec bxx vec c)a n d vec V_2=( vec axx vec b)xx vec c. Vectors vec V_1a n d vec V_2 are equal. Then (a). vec aa n vec b are orthogonal (b). vec aa n d vec c are collinear (c). vec ba n d vec c are orthogonal (d). vec b=lambda( vec axx vec c)w h e nlambda is a scalar

If vec A, vec B and vec C are vectors such that |vec B|=|vec C| . Prove that [(vec A+ vec B)xx (vec A + vec C)]xx (vec B+vec C).(vec B+ vec C)=0