If a, b, c are non-coplanar vectors such that`x_1 vec a+y_1 vec b+z_1 vec c=x_2 vec a+y_2 vec b+z_2 vec c ,` prove that `x_1=x_2, y+1=y+2a n dz_1=z_2dot`

veca , vec b , vec c are non-coplanar vectors and x vec a + y vec b + z vec c = vec 0 then

If a and b ar non collinear vector such that x_(1)vec a+y_(1)vec b=x_(2)vec a+y_(2)vec b, then prove that x_(1)=x_(2) and y_(1)=y_(2) .

If vec a,vec b, and vec c are non-coplanar unit vectors such that vec a xx(vec b xxvec c)=(vec b+vec c)/(sqrt(2)),vec b and vec c are non parallel,then prove that the angel between vec a and vec b is 3 pi/4

Let vec a , vec b ,vec c are three non- coplanar vectors such that vecr_(1)=veca + vec c , vecr_(2)= vec b+vec c -veca , vec r_(3) = vec c + vec a + vecb, vec r = 2 vec a - 3 vec b + 4 vec c. If vec r = lambda_(1)vecr_(1)+lambda_(2)vecr_(2)+lambda_(3)vecr_(3) , then

If vec a, vec b, vec c and vec d are unit vectors such that (vec a xxvec b) * (vec c xxvec d) = 1 and vec a * vec c = (1) / (2)

If vec b and vec c are two non-collinear vectors such that vec a*(vec b+vec c)=4 and vec a xx(vec b xxvec c)=(x^(2)-2x+6)vec b+(sin y)vec c then the point (x,y) lies on

If vec a,vec b and vec c are three non-zero vectors,prove that [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 any three non-coplanar vectors,then prove that points l_(1)vec a+m_(1)vec b+n_(1)vec c,l_(2)vec a+m_(2)vec b+n_(2)vec c,l_(3)vec a+m_(3)vec b+n_(3)vec c,l_(4)vec a+m_(4)vec b+n_(4)vec c are coplanar if [[n_(1),n_(2),n_(3),n_(4)1,1,1,1]]=0

vec a, vec b, vec c are three non-zero vectors. If o + be defined as vec x o + vec y = vec x + vec y + vec x xxvec y and

undersetvec x + thenvec x + vec y = vec a, vec x xxvec y = vec b and vec x * vec a = 1