find eqaution of a plane

**ramzouzy** · March 11th 2008, 06:59 PM

find the equation of the plane that goes through (1,2,-1) and making equal angles with the positive directions of the coordinate axes

**Soroban** · March 11th 2008, 09:38 PM

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: . $\vec{n} \:=\:\langle1,1,1\rangle$
Hence, its equation has the form: . $(x-x_1) + (y-y_1) + (z-z_1) \:=\:0$

Since (1,2,-1) is on the plane: . $(x-1) + (y-2) + (z+1) \:=\:0$

Therefore: . $\boxed{x + y + z \:=\:2}$

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