## Thomas' Calculus 13th Edition

$x+y+2z=3$
Formula to calculate the vector equation is:$\nabla f(r_0) \cdot (r-r_0)=0$ As we know that the equation of tangent for $\nabla f( 1,1,\dfrac{1}{2})=\lt -\dfrac{1}{2},-\dfrac{1}{2},-1 \gt$ is given by $-\dfrac{1}{2}(x-1)-\dfrac{1}{2}(y-1)-1(z-\dfrac{1}{2})=0$ or, $-(\dfrac{1}{2})x+\dfrac{1}{2}-(\dfrac{1}{2})y+\dfrac{1}{2}-z+(\dfrac{1}{2})=0$ Thus, $x+y+2z=3$