Find an equation of the given plane. The plane containing the point with normal vector
A) 3x + y + 7z = -22
B) 2x + 7y - 5z = 0
C) 2x + 7y - 5z = -22
D) 2x + 7y - 5z = 11

Question

Find an equation of the given plane. The plane containing the point  with normal vector 
A) 3x + y + 7z = -22 
B) 2x + 7y - 5z = 0 
C) 2x + 7y - 5z = -22 
D) 2x + 7y - 5z = 11

Quizplus · Accepted Answer

The equation of a plane in standard form is Ax + By + Cz = D, where (A, B, C) is the normal vector to the plane, and D is a constant. 
Given point = (11eaa88b_93b8_21f2_a696_d7d8507c22d6_TB5869_11)
Normal vector = (11eaa88b_93b8_21f3_a696_319e83c26385_TB5869_11)
Substituting these values in the standard form equation: 
2x + 7y - 5z = D
To find D, we use the point on the plane: 
2(11) + 7(10) - 5(-1) = D
D = -22
So the equation of the plane is: 
2x + 7y - 5z = -22, which is choice C.

Find an Equation of the Given Plane