Show that the normal vector to the plane 2x + 2y + 2z = 3 is equally inclined with the coordinate axes.

Question

Philoid · Accepted Answer

The vector equation of the plane 2x + 2y + 2z = 3 can be written as

The normal to this plane is

Direction ratio of

Direction cosine of

So,

Let be the angle that normal makes with the coordinate axes respectively

Similarly,

Hence

So the normal vector to the plane 2x + 2y + 2z = 3 is equally inclined with the coordinate axes.