Find an equation of the given plane. The plane containing the point with normal vector
A) -5x - 3y + 9z = -30
B) 9x - 8y - z = 0
C) 9x - 8y - z = -30
D) 9x - 8y - z = 1

Question

Find an equation of the given plane. The plane containing the point  with normal vector 
A) -5x - 3y + 9z = -30 
B) 9x - 8y - z = 0 
C) 9x - 8y - z = -30 
D) 9x - 8y - z = 1

Quizplus · Accepted Answer

The equation of a plane can be written in the form 
Ax + By + Cz = D, 
where A, B, and C are the components of the normal vector and (x, y, z) is any point on the plane. 
Substituting the given values, we get 
9x - 8y - z = D. 
To find D, we can plug in the coordinates of the point on the plane: 
9(11) - 8(cdc1) - (0f147ad1) = D 
99 - 329 + 258 = D 
D = -30 
Therefore, the equation of the plane is 
9x - 8y - z = -30, which is choice C.

Find an Equation of the Given Plane