Finding Solutions for the Intersection of a Plane and Line

In summary, the problem is to find points on the intersection of a given plane and a line, represented by the equation Ax=d, where A is a 3x3 matrix and x and d are vectors. The goal is to find a specific matrix A and vector d that will give the coordinates of the point of intersection between the two objects. This can be achieved by solving a system of equations related to the given plane and line.
  • #1
lukepeterpaul
14
0

Homework Statement


hi, i have been given a question and would appreciate help in interpreting it.
given a plane, state the problem of finding points on the intersection of the plane and the line in the form Ax=d, where A is a 3by3 matrix, x and d are vectors.

Homework Equations





The Attempt at a Solution


i don't understand the question...
i m guessing that it is referring to the specific circumstance when matrix A has rank 2...??
in fact the question then proceeds to "find and interpret the solutions"...
 
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  • #2
Well, I interpret the question this way: a plane can be described by an equation. A line can be describe by a system of equations.

Now, the line and the plane intersect in a point. This point can be found by a system of equations (which are of course closely related to the equations above). This system of equations can be written under the form Ax=d. So, you need to find a matrix A and a matrix d, such that the intersection of the plane and the line is the solution to Ax=d.

Hope that was helpful...
 
  • #3
cheers :)
 

FAQ: Finding Solutions for the Intersection of a Plane and Line

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Interpreting a question is a crucial step in the scientific process as it helps researchers to understand the question being asked and formulate an appropriate answer. It allows for a clear understanding of the problem at hand and helps to guide the research process.

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