Write the equation for the plane.
-The plane through the point A(2, 10, 8) perpendicular to the vector from the origin to A.
A) $2 x + 10 y + 8 z = \sqrt { 168 }$
B) $2 x + 10 y + 8 z = 168$
C) $2 x + 10 y + 8 z = - 168$
D) $2 x + 10 y + 8 z = 20$

Question

Write the equation for the plane.
-The plane through the point A(2, 10, 8) perpendicular to the vector from the origin to A. 
A) $2 x + 10 y + 8 z = \sqrt { 168 }$
B) $2 x + 10 y + 8 z = 168$
C) $2 x + 10 y + 8 z = - 168$
D) $2 x + 10 y + 8 z = 20$

Quizplus · Accepted Answer

The equation of a plane can be written as ax + by + cz = d, where (a,b,c) is the normal vector to the plane. In this case, the normal vector is the vector from the origin to A, which is (2, 10, 8). Therefore, the equation of the plane is 2x + 10y + 8z = d. To find d, we can use the coordinates of point A: 2(2) + 10(10) + 8(8) = 168. Thus, the equation of the plane is 2x + 10y + 8z = 168, which is choice B.

Write the Equation for the Plane 2x+10y+8z=1682 x + 10 y + 8 z = \sqrt { 168 }2x+10y+8z=168​

Write the Equation for the Plane $2 x + 10 y + 8 z = \sqrt { 168 }$