The discussion focuses on finding the equation of the line of intersection between two planes defined by the equations 2x + 3y + 5z = 2 and 4x + 2y + z = 11. It is established that there is a unique line of intersection, and the equation of this line will involve a parameter, typically one of the variables, such as z. The solution process involves expressing two variables in terms of the third, allowing for a parametric representation of the line.
PREREQUISITESStudents of mathematics, educators teaching geometry, and anyone interested in understanding the intersection of planes in three-dimensional space.
debwaldy said:Hello,so this is prob a v v basic question but I am confused as to how one find the equation of the line of intersection of two planes:e.g. 2x + 3y + 5z = 2 & 4x + 2y + z = 11. is there just one unique solution or will the solution involve parameters??eeks
The question asks for the line at which the two planes intersect. Yes there is a unique line of intersection and, yes, the equation of a line in 3 dimensions involves a parameter!