MHB Where Do These Parametric Equations and Plane Intersect?

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To find the intersection of the parametric equations and the plane, substitute x, y, and z from the equations into the plane equation -2x + 8y + 8z = 10. This leads to the equation -2(-5 + 8t) + 8(1 + 10t) + 8(9 + 8t) = 10. Simplifying this will yield a value for t, which can then be used to find the corresponding x, y, and z coordinates. The intersection point can be determined by solving for t and substituting back into the parametric equations. This process effectively identifies where the parametric line intersects the defined plane.
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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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