Question
Asked Sep 11, 2019
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I am working with cal 3. How do I find the parametric equations of the line for the intersection of two planes: 5x − 4y + z = 1,     4x + y − 5z = 5?

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Expert Answer

Step 1

The parametric equations of a line through the point (x0, y0, z0) and parallel to the direction vector (a, b, c) is

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x = xo +at, y = yo + bt,2 (1) oct

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Step 2

Given equations of planes are,

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5х - 4у+:%3D1 (2) (3) 4х+ у - 52 %3D5

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Step 3

Substitute z = 0 in equations (2)...

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5x — 4у%3D1 (4) (5) 4х + у 3D5

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