Determine a vector that is parallel to the plane:
x + 2y + 2z - 5 = 0
A vector formed by joining any two points that lie in the plane is parallel to the plane.
For example, for the given plane
P: x + 2y + 2z - 5 = 0
A(1,1,1) lies in the P, and
B(5,0,0) lies in the P.
Therefore the vector
BA = (1-5, 1-0, 1-0) = (-4, 1, 1)
is parallel to the given plane.
To determine a vector that is parallel to a plane, you need to find the normal vector of the plane.
The equation of the plane is given in the form Ax + By + Cz + D = 0, where A, B, and C are the coefficients of x, y, and z, respectively. In this case, the coefficients are:
A = 1
B = 2
C = 2
The normal vector of the plane is then simply the coefficients A, B, and C. So, the vector that is parallel to the plane x + 2y + 2z - 5 = 0 is:
<1, 2, 2>