find the equation of the plane that goes through (1,2,-1) and making equal angles with the positive directions of the coordinate axes
Hello, ramzouzy!
Find the equation of the plane that goes through (1,2,-1) and
makes equal angles with the positive directions of the coordinate axes
This plane is tilted so there is an equilateral triangle in the first octant.
. . It has normal vector: .$\displaystyle \vec{n} \:=\:\langle1,1,1\rangle$
Hence, its equation has the form: .$\displaystyle (x-x_1) + (y-y_1) + (z-z_1) \:=\:0$
Since (1,2,-1) is on the plane: .$\displaystyle (x-1) + (y-2) + (z+1) \:=\:0$
Therefore: .$\displaystyle \boxed{x + y + z \:=\:2}$