If `x=c y+b z ,y=a z+c x ,z=x+a y ,w h e r e .x ,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),w h e r e .x , y and z are not all zero, then the value of a b+b c+c a is a. 0 b. 1 c. -1"" d. none of these

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

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

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

Value of |x+y z z x y+z x y y z+x|,w h e r ex ,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 the equation of plane containing the line x-y+z=0a n dx+y+z-2=0 and which is farthest from origin is a x+b y+c z=d ,w h e r ea , b ,c ,d in N , then find the minimum value of (a+b+c+d)dot

If the system of equations x=c y+b z ,\ \ y=a z+c x ,\ \ z=b x+a y has a non-trivial solution show that a^2+b^2+c^2+2a b c=1

If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

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 a. x y z b. 2x y z c. 3x y z d. 4x y z

If the system of equations x=c y+b z y=a z+c x z=b x+a y has a non-trivial solution, show that a^2+b^2+c^2+2a b c=1