Not sure on how to approach this any pointers or can you lead me in the right di
ID: 3856523 • Letter: N
Question
Not sure on how to approach this any pointers or can you lead me in the right direction
You may use a computer algebra system (such as Mathematica, Matlab, etc)or a programming language (such as C++, Java, etc) or possibly some other appropriate software of your choice. The words "A point (a vector) is given" mean that its coordinates (components) are given. The words "A line is given" mean that its equation is given. You can use as an input either equation of the line in some form or its initial point and direction vector. The words "A plane is given" mean that its general equation is given. You can use as an input either this equation or the vector of coefficients. The words "Determine .., find .. " mean that you are asked to create a program (or some kind of software implementation) that takes as input the given data and returns the required equations. Submit a paper that includes: a nice cover sheet, an explanation of the mathematical principles used in your programs, and a printout of sample runs of the programs. Keep the programs on your computers. Later I will set up short meetings with you to check how your programs work on inputs selected by me. A line l and a plane pi in R^3 are given. Determine whether the line l lies in the plane pi, parallel to this plane, or intersects this plane. If l intersects pi, find the point of intersection.Explanation / Answer
To determine if line l lies in plane , replace x, y, and z in the equation of the plane with their expressions in terms of some parameter. That will give a single linear equation for that parameter. If the equation is satisfied by a single value of the parameter, the line intersects the plane and that value of the parameter gives the point of intersection. If no value of the parameter satisfies the equation, the line is parallel to the plane. If the equation is satisfied for every member of the parameter, the line lies in the plane.
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