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Find equations for the following: (a) The plane which passes through the point (0,0,1) which is...

Question:

Find equations for the following:

(a) The plane which passes through the point (0,0,1) which is also orthogonal to the two planes

{eq}x=2 {/eq} and

{eq}y=19. {/eq}

(b) The plane parallel to the plane

{eq}2x-3y=0[{Image src='e644dd78ee05cf81174dd9582155a7114553539550605669925.jpg' alt='' caption=''}] {/eq} and passing through the point (2,3,2).

(c) The plane containing the

{eq}x {/eq}-axis and the point (1,1,1).

Normal to a plane

Normal to a plane a plane that is given by a scalar {eq}f(x,y,z)=0 {/eq}, is given by the gradient of f, as follows,

{eq}\nabla f(x,y,z)=\frac{\partial f}{\partial x}i+\frac{\partial f}{\partial y}j+\frac{\partial f}{\partial z}k {/eq}

Answer and Explanation:

a)

The vector normal to the plane {eq}f1: x-2=0 {/eq} is given by {eq}\nabla f1=i {/eq}

The vector normal to the plane {eq}f2: y-19=0 {/eq} is...

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Directional Derivatives, Gradient of f and the Min-Max

from GRE Math: Study Guide & Test Prep

Chapter 14 / Lesson 6
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