Find a unit vector parallel to the line of intersection of the planes given by the equations 3x -...

Question:

Find a unit vector parallel to the line of intersection of the planes given by the equations {eq}3x - 4y + 5z = 3 {/eq} and {eq}4x + y - 3z = 7 {/eq}.

Intersection of Two Given Planes:

Given two planes, we first find a vector normal to each plane. The cross-product (say {eq}\mathbf{L} {/eq}) of the two normal vectors is parallel to the line formed by the intersection of two given planes. The unit vector in the direction of {eq}\mathbf{L} {/eq} is obtained by dividing {eq}\mathbf{L} {/eq} by its magnitude.

Answer and Explanation:

Answer: {eq}\displaystyle \frac {\langle 7,\,29,\,19 \rangle}{35.369} {/eq}.


Explanation:

Normal to the plane {eq}P:\,3x - 4y + 5z = 3 {/eq} is...

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Learn more about this topic:

Lines & Planes in 3D-Space: Definition, Formula & Examples

from GRE Math: Study Guide & Test Prep

Chapter 13 / Lesson 6
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