The equation of the plane through (2,3,-1) normal to the line $\frac { x - 1 } { 2 } = \frac { y - 1 } { 3 } = \frac { z + 1 } { - 2 }$ is

A) $2 x + 3 y - 2 z = 14$
B) $2 x + 3 y - 2 z = 15$
C) $2 x + 3 y - 2 z = - 14$
D) $2 x + 3 y - 2 z = - 15$
E) $2 x + 3 y - 2 z = 13$

Question

The equation of the plane through (2,3,-1) normal to the line $\frac { x - 1 } { 2 } = \frac { y - 1 } { 3 } = \frac { z + 1 } { - 2 }$ is

A) $2 x + 3 y - 2 z = 14$
B) $2 x + 3 y - 2 z = 15$
C) $2 x + 3 y - 2 z = - 14$
D) $2 x + 3 y - 2 z = - 15$
E) $2 x + 3 y - 2 z = 13$

Quizplus · Accepted Answer

The direction ratios of the line are (2, 3, -2). The equation of the plane with these direction ratios as the normal vector passing through the point (2, 3, -1) is $2(x-2) + 3(y-3) - 2(z+1) = 0$, which simplifies to $2x + 3y - 2z = 15$.

The Equation of the Plane Through (2,3,-1) Normal to the Line