SUMMARY
The intersection of two perpendicular planes is represented by the line equation r=(-1+5t)i +(5-t)j +(7-4t)k, with one plane defined by the equation 5x-3y+7z=29. The second plane's rectangular equation is derived by identifying a point on the plane, specifically (-1, 5, 7), and calculating the cross product of the direction vector (5, -1, -4) and the normal vector of the first plane (5, -3, 7). The final normal equation for the second perpendicular plane is 19x+55y+10z=326.
PREREQUISITES
- Understanding of vector equations in three-dimensional space
- Knowledge of plane equations and their normal vectors
- Familiarity with the cross product of vectors
- Ability to derive rectangular equations from parametric forms
NEXT STEPS
- Study the properties of vector equations in 3D geometry
- Learn how to compute the cross product of vectors in detail
- Explore the derivation of plane equations from parametric forms
- Investigate applications of perpendicular planes in geometric problems
USEFUL FOR
Mathematicians, physics students, and engineers working with three-dimensional geometry, particularly those focusing on vector analysis and plane equations.
