If `x=c y+b z ,y=a z+c x ,z=x+a y ,w h e r ex ,y ,z` are not all zeros, then find the value of `a^2+b^2+c^2+2a b c dot`

Given a=x/(y-z),b=y/(z-x), and c=z/(x-y), where x,y,z and are not all zero,then the value of ab+bc+ca is 0 b.1 c.-1 none of these

If (xy)/(x+y)=a,(xz)/(x+z)=b and (yz)/(y+z)=c where a,b,c are other than zero,find the value of x

Points A( vec a),B( vec b),C( vec c)a n dD( vec d) are relates as x vec a+y vec b+z vec c+w vec d=0 and x+y+z+w=0,w h e r ex ,y ,z ,a n dw are scalars (sum of any two of x ,y ,zn a dw is not zero). Prove that if A ,B ,Ca n dD are concylic, then |x y|| vec a- vec b|^2=|w z|| vec c- vec d|^2dot

Value of [[x+y, z,z ],[x, y+z, x],[y, y, z+x]], where x ,y ,z are nonzero real number, is equal to x y z b. 2x y z c. 3x y z d. 4x y z

If x= b+c, y=c+a, z=a+b , then find the value of (x^2 + y^2 + z^2 -yz - zx-xy)/( a^(2) + b^(2) + c^(2) - bc - ca - ab)

If a+b=z, c+a=y, b+c=x, x^(2)+y^(2)+z^(2)=50 and xy+yz+zx=47 then find the value of a^(2)+b^(2)+c^(2)+ab+bc+ca .