If `x=c y+b z ,y=a z+c x ,z=bx+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),a n dc=z//(x-y),w h e r ex , y , za n dz are not all zero, then the value of a b+b c+c a is 0 b. 1 c. -1"" d. none of these

If y z+z x+x y=12 ,w h e r ex ,y ,z are positive values, find the greatest value of x y zdot

If the planes x-c y-b z=0,c x-y+a z=0a n d b x+a y-z=0 pass through a straight line, then find the value of a^2+b^2+c^2+2a b c dot

If a^x=b ,b^y=c ,c^z=a , then find the value of x y zdot

In the adjacent figure, find the value of x, y, z and a, b, c.

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

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

The value of |[yz, z x,x y],[ p,2q,3r],[1, 1, 1]|,w h e r ex ,y ,z are respectively, pth, (2q) th, and (3r) th terms of an H.P. is a. -1 b. 0 c. 1 d. none of these

Prove that |a x-b y-c z a y+b x c x+a z a y+b x b y-c z-a x b z+c y c x+a z b z+c y c z-a x-b y|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

If x,y,z are in G.P and a^x=b^y=c^z ,then