Find the Intersection Point of a Line and Plane: Step by Step Guide

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SUMMARY

The discussion focuses on finding the intersection point of a line and a plane using specific equations. The line is defined by the parametric equations x = -4t + 4, y = -4t + 6, and z = 5t + 5, while the plane is represented by the equation 4x - 2y + 6z = 78. To determine the intersection, one must substitute the line's equations into the plane's equation, resulting in a linear equation in terms of t. Solving for t allows for the calculation of the intersection coordinates by substituting t back into the line's equations.

PREREQUISITES
  • Understanding of parametric equations
  • Familiarity with linear equations
  • Basic knowledge of algebraic substitution
  • Concept of geometric intersection in three-dimensional space
NEXT STEPS
  • Practice solving parametric equations with different lines and planes
  • Learn about vector equations and their applications in geometry
  • Explore methods for visualizing intersections in 3D space
  • Study the implications of intersection points in physics and engineering contexts
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Students studying geometry, mathematics educators, and anyone interested in understanding the intersection of lines and planes in three-dimensional space.

lakitu
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coordinate help please :)

Hi i just got my home work but don't know where to start. Any help on this just to get me started would be great:) I want to make sure I am doing it right

Thank you


Work out the coordinates where this line meets this plane.

Line x = -4 t + 4, y = -4 t + 6, z = 5 t + 5 and plane 4 x - 2 y + 6 z = 78.
 
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Plug your expressions for x,y,z into the plane definition. You now have an equation (linear) for t. Solve for t and plug it into your x,y,z definitions for the line.
 
hey thank you for replying i will give that a go :)
 

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