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 x xx 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 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 vec a and vec b are two non-collinear unit vectors such that | vec a+ vec b|=sqrt(3), find (2 vec a-5 vec b). (3 vec a+ vec b) .

If vec a\ a n d\ vec b are two non collinear unit vectors such that | vec a+ vec b|=sqrt(3),\ find \ (2 vec a-5 vec b). (3 vec a+ vec b)

Let vec aa n d vec b be two non-zero perpendicular vectors. A vecrtor vec x satisfying the equation vec x xx vec b= vec a is vecx= beta vecb-1/|b|^2 vecaxx vecb then beta can be

If vec xa n d vec y are two non-collinear vectors and a, b, and c represent the sides of a A B C satisfying (a-b) vec x+(b-c) vec y+(c-a)( vec x xx vec y)=0, then A B C is (where vec xxx vec y is perpendicular to the plane of xa n dy ) a. an acute-angled triangle b. an obtuse-angled triangle c. a right-angled triangle d. a scalene triangle

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

If vec a, vec b , vec c are three non- coplanar vectors such that vec a + vec b + vec c = alpha vec d and vec b +vec c + vec d = beta vec a, " then " vec a + vec b + vec c + vec d to equal to

If vec a ,\ vec b ,\ vec c are non coplanar vectors, prove that the following vectors are non coplanar: \ 2 vec a- vec b+3 vec c ,\ vec a+ vec b-2 vec c\ a n d\ vec a+ vec b-3 vec c

If vec a ,\ vec b ,\ vec c are non coplanar vectors, prove that the following vectors are non coplanar: \ vec a+2 vec b+3 vec c ,\ 2 vec a+ vec b+3 vec c\ a n d\ vec a+ vec b+ vec c

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