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Dethrone
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Yep, now apply the methods of checking I mentioned above. (Nod)
How can we determine the intersection point of two lines with given equations?
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- Thread starter ineedhelpnow
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SUMMARY
This discussion focuses on determining the intersection point of two lines represented by the equations $L_1: \frac{x-2}{1}= \frac{y-3}{-2}= \frac{z-1}{-3}$ and $L_2: \frac{x-3}{1}= \frac{y+4}{3}= \frac{z-2}{-7}$. The lines are analyzed for parallelism, skewness, and intersection using vector direction analysis and parametric equations. The conclusion reached is that the lines are skew, as no common point of intersection exists, confirmed by the inability to solve for parameters $s$ and $t$ that satisfy all equations simultaneously.
PREREQUISITES- Understanding of vector representation in 3D space
- Knowledge of parametric equations for lines
- Familiarity with the concepts of parallel, skew, and intersecting lines
- Ability to perform algebraic manipulations such as substitution and elimination
- Study the method of solving systems of equations using elimination and substitution techniques
- Learn about the geometric interpretation of vectors and their applications in 3D space
- Explore the concept of skew lines in greater detail, including examples and visualizations
- Investigate the conditions under which two lines in 3D space can intersect
Students and professionals in mathematics, physics, and engineering who are working with vector equations and need to determine line relationships in three-dimensional space.
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