If ` vec x , vec y` are two non-zero and non-collinear vectors satisfying `[(a-2)alpha^2+(b-3)alpha+c] vec x+[(a-2)beta^2+(b-3)beta+c] vec y+[(a-2)gamma^2+(b-3)gamma+c]( vec xxx vec y)=0, w h e r ealpha,beta,gamma` are three distinct real numbers, then find the value of `(a^2+b^2+c^2-4)dot`

If vecx, vecy are two non-zero and non-collinear vector satisfying [(a-2)alpha^(2) +(b-3)alpha +c]vecx -2beta^(2) + beta -3beta - alpha]vecy +[(a -2)gamma^(2) + (b-3)y + c](vec(x) xx vecy)=0 , where alpha, beta, gamma are three distinct real numbers, then find the value of (a^(2) + b^(2) + c^(2)-4) .

If vecx and vecy are two non zero, non - collinear vectors satisfying ((a-3)alpha^(2)+(b-4)alpha+(c-1))vecx +[(a-3)beta^(2)+(b-4)beta+(c-1)]vecy+[(a-3)gamma^(2)+(b-4)gamma+(c-1)](vecx xx vecy)=0 (where alpha, beta,gamma are three distinct numbers), then the value of (a^(2)+b^(2)+c^(2))/(4) is equal to

If quad vec r = alpha (vec b xxvec c) + beta (vec c xxvec a) + gamma (vec a xxvec b) and [vec with bvec c] = 2 then alpha + beta + gamma

vec a and vec b are two non-collinear vectors then the value of {(vec a)/(|vec a|^(2))-(vec b)/(|vec b|^(2))} is equal to

If (vec a xxvec b)+beta(vec b xxvec c)+gamma(vec c xxvec a)=0 and at least of the numbers alpha,beta and gamma is non- zero,then the vectors vec a,vec b and vec c are

Let a & b be two non-zero perpendicular vectors.If a vector vec x satisfying the equation vec x xxvec b=vec a is vec x=beta b-(a xx b)/(|vec b|^(2)) then beta can be

If vec a and vec b are non-collinear vectors,find the value of x for which the vectors vec alpha=(2x+1)vec a-vec b and vec beta=(x-2)vec a+vec b are collinear.

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 and vec b are non-collinear vectors,then the value of x for which vectors vec alpha=(x-2)vec a+vec b and vec beta=(3+2x)vec a-2vec b are collinear,is given by

If vec a and vec b are non-collinear vectors and vectors vec alpha=(x+4y)vec a+(2x+y+1)vec b and vec beta=(-2x+y+2)vec a+(2x-3y-1)vec b are connected by the relation 3vec alpha=2vec beta ,find the value of x and y?