# Find the cosine of the angle between the planes -4x +4y -4z = -3 and the plane 2x -4y - 1z = 3

## Question:

Find the cosine of the angle between the planes {eq}-4x +4y -4z = -3 {/eq} and the plane {eq}2x -4y - 1z = 3 {/eq} .

## Angle Between The Planes:

The angle {eq}\theta {/eq} between the planes {eq}\displaystyle a_{1}x + b_{1}y +c_{1} z = d_{1} \enspace and \enspace a_{2}x + b_{2}y +c_{2} z = d_{2} {/eq} is

{eq}\displaystyle \cos \theta =\frac {a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}}{\sqrt{a_{1}^2 +b_{1}^2 +c_{1}^2} \sqrt{a_{2}^2 + b_{2}^2 +c_{2}^2}} {/eq}

## Answer and Explanation:

The angle {eq}\theta {/eq} between the planes {eq}-4x +4y -4z = -3 \enspace and \enspace 2x -4y - 1z = 3 {/eq} is

{eq}\begin{align*}\cos \theta...

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from Basic Geometry: Help & Review

Chapter 2 / Lesson 4