Find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line.
Point: $( 7,8,2 )$ Perpendicular to: $\mathbf { n } = - 4 \mathbf { i } + \mathbf { j } - 5 \mathbf { k }$
A) $- 4 x + - 4 y - 5 z + 30 = 0$
B) $- 4 y - 5 z + 30 = 0$
C) $- 4 x + y 30 z + - 5 = 0$
D) $- 4 x + y - 5 z + 30 = 0$
E) $- 4 x + y - 5 z - 30 = 0$

Question

Find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line. 
Point: $( 7,8,2 )$ Perpendicular to: $\mathbf { n } = - 4 \mathbf { i } + \mathbf { j } - 5 \mathbf { k }$ 
A) $- 4 x + - 4 y - 5 z + 30 = 0$
B) $- 4 y - 5 z + 30 = 0$
C) $- 4 x + y 30 z + - 5 = 0$
D) $- 4 x + y - 5 z + 30 = 0$
E) $- 4 x + y - 5 z - 30 = 0$

Quizplus · Accepted Answer

The equation of a plane in vector form is given by $n \cdot (r - r_0) = 0$, where $n$ is the normal vector to the plane, $r$ is the position vector of any point on the plane, and $r_0$ is the position vector of a given point on the plane. Given $n = -4\mathbf{i} + \mathbf{j} - 5\mathbf{k}$ and the point $(7,8,2)$, the equation becomes $-4(x-7) + 1(y-8) - 5(z-2) = 0$, which simplifies to $-4x + y - 5z + 30 = 0$.

Find the General Form of the Equation of the Plane (7,8,2)( 7,8,2 )(7,8,2)

Find the General Form of the Equation of the Plane $( 7,8,2 )$