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

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- Mar 11th 2008, 06:59 PMramzouzyfind eqaution of a plane
find the equation of the plane that goes through (1,2,-1) and making equal angles with the positive directions of the coordinate axes

- Mar 11th 2008, 09:38 PMSoroban
Hello, ramzouzy!

Quote:

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