# Equation of the plane S

• -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 .

## The Attempt at a Solution

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

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.

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

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?

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