Where Do These Parametric Equations and Plane Intersect?

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SUMMARY

The intersection of the parametric equations x = -5 + 8t, y = 1 + 10t, z = 9 + 8t and the plane defined by the equation -2x + 8y + 8z = 10 can be found by substituting the parametric equations into the plane equation. By replacing x, y, and z in the plane equation, the resulting equation can be solved for the parameter t, which will yield the specific point of intersection in three-dimensional space.

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Find the intersection.

x = -5 + 8t, y = 1 + 10t, z = 9 + 8t ; -2x + 8y + 8z = 10
 
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aa1604962 said:
Find the intersection.

x = -5 + 8t, y = 1 + 10t, z = 9 + 8t ; -2x + 8y + 8z = 10

Start by replacing x with -5 + 8t, y with 1 + 10t, and z with 9 + 8t, in your plane.
 

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