Answer
(a) $x+y+z=3$
(b) $\frac{x-1}{2}=\frac{y-1}{2}=\frac{z-1}{2}$
Work Step by Step
$xy+yz+zx=3 ; (1,1,1)$
(a) Equation for a tangent plane is given as:
$z-1=-(x-1)-(y-1)$
$z-1=-x-1-y+1$
$x+y+z=3$
(b) $x+y+z=3$
Equation of normal line is:
$\frac{x-1}{2}=\frac{y-1}{2}=\frac{z-1}{2}$
