Finding the Equation of a Plane in a 3D Space

[-EquinoX-]

Homework Statement

S is the square of side 2 with one vertex at the origin, one edge along the positive y-axis, one edge in the xz-plane with x ≥ 0, z ≥ 0, and the normal is n = i - k .

Homework Equations

The Attempt at a Solution

Can someone help me how to find the equation of this plane?

 

[HallsofIvy]

One vertex is the origin, (0, 0, 0), and you know the normal vector. What more do you need? The plane containing the point (x₀, y₀, z₀), with normal vector <A, B, C>, has equation A(x- x₀)+ B(y- y₀)+ C(z- z₀)= 0.

 

[-EquinoX-]

yes.. I tried (0,0,0) and I got x - z = 0 ? is this true?

 

[HallsofIvy]

Strictly speaking, a "square" is not a plane, it lies in a plane, so this is a strangely worded question!

Certainly, the origin, the corner (0,0,0) satisfies x- z= 0, the edge along the positive y- axis, (0, y, 0) satisfies x- z= 0, and the edge in the xz-plane, satisfying x- z= 0, (x, 0, x) is at right angles to (0, y, 0) (because <0, y, 0>.<x, 0, x>= 0). What more do you want?