What is the unit normal to the plane z10x24y32 at point 2 1

Solution

Given z=-10x+24y+32
and point (2,-1,-12)
to find the unit normal to the plane first calculate the magnitude

(a²+b²+c²)=[(10*10)+(24*24)]

=(100+576)

=26

unit normal to the plane= (-10x+24y+32)/26 at point (2,-1,-12)

=[(-10*2)+(24*(-1))+32]/26

=(-20-24+32)/26

=-12/26

=-0.461