# Chapter 12 - Vectors and the Geometry of Space - 12.5 Equations of Lines and Planes - 12.5 Exercises - Page 871: 28

$x+y-z=-7$

#### Work Step by Step

The general form of the equation of the plane is: $a(x-x_0)+b(y-y_0)+c(z-z_0)=0$ or, $ax+by+cz=ax_0+by_0+cz_0$ The required equation of the required plane is of the form: $z=x+y+k$ Put $x=3,y=-2, z=8$ and solve for $k$. After simplification, we get $8=3-2+k$ $k=7$ Hence, $x+y+7=z$ or, $x+y-z=-7$

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