Write the equation for the plane.
-The plane through the point A(-5, -2, 4) perpendicular to the vector from the origin to A.
A) $- 5 x - 2 y + 4 z = - 45$
B) $5 x + 2 y - 4 z = - 45$
C) $5 x + 2 y - 4 z = \sqrt { 45 }$
D) $5 x - 2 y - 4 z = 3$

Question

Write the equation for the plane.
-The plane through the point A(-5, -2, 4) perpendicular to the vector from the origin to A. 
A) $- 5 x - 2 y + 4 z = - 45$
B) $5 x + 2 y - 4 z = - 45$
C) $5 x + 2 y - 4 z = \sqrt { 45 }$
D) $5 x - 2 y - 4 z = 3$

Quizplus · Accepted Answer

The equation for a plane can be written as Ax + By + Cz = D, where (A, B, C) is the normal vector to the plane. Since the plane is perpendicular to the vector from the origin to A, the normal vector will be the same as that vector, which is <5, 2, -4>. So the equation of the plane is 5x + 2y - 4z = D. To find D, we can substitute the coordinates of A into the equation and solve for D: 5(-5) + 2(-2) - 4(4) = D. This simplifies to -45 = D, so the final equation is 5x + 2y - 4z = -45. Therefore, the best choice is B.

Write the Equation for the Plane −5x−2y+4z=−45- 5 x - 2 y + 4 z = - 45−5x−2y+4z=−45

Write the Equation for the Plane $- 5 x - 2 y + 4 z = - 45$