What is the Projection of Line M_1P on Plane \pi?

In summary, the conversation discusses finding the projection of the line M_1P on the plane given by the equation \pi and the point M=(1,2,3) outside the plane. The individual is unsure of how to proceed after finding the equation of the plane and asks for help. The other person suggests using the plane normal vector and doing an experiment with a pen on a desk to better understand the concept. They also ask for clarification on what M_1 represents and suggest finding the point P first.
  • #1
chmate
37
0

Homework Statement



Given [tex]\pi: \begin{cases}l_1: \frac{x-2}{4}\ = \frac{y-1}{2}\ = \frac{z+5}{-4} &\\l_2: \frac{x+4}{-2}\ = \frac{y+1}{0}\ = \frac{z}{1} & \end{cases}[/tex] and the point [tex]M=(1,2,3)[/tex] outside the plane. Find the projection of the line [tex]M_1P[/tex] on plane [tex]\pi[/tex] where [tex]P[/tex] is the intersection point of lines [tex]l_1, l_2[/tex].2. The attempt at a solution

All I can do is that I can find the equation of plane [tex]\pi[/tex] but don't have any idea what to do next. So I need your help.

Thank you.
 
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  • #2
How can you use the plane normal vector ?
Just make some "expriment" with a pen on your desk as a plane.
 
  • #3
What is [itex]M_1[/itex]? You never defined what it is.

Start by finding P.
 

1. What is the purpose of projecting a line on a plane?

The purpose of projecting a line on a plane is to determine the location of the line on the plane and its relationship to other elements on the plane. This can be useful in various fields such as engineering, architecture, and mathematics.

2. How is a line projected on a plane?

A line is projected on a plane by extending the line until it intersects with the plane. The point of intersection is then marked as the projected point of the line on the plane.

3. What is the difference between a parallel and perpendicular projection of a line on a plane?

A parallel projection of a line on a plane is when the line is projected onto the plane without changing its direction. A perpendicular projection, on the other hand, is when the line is projected onto the plane at a 90 degree angle, resulting in a change in its direction.

4. How is the length of a projected line on a plane determined?

The length of a projected line on a plane is determined by measuring the distance from the starting point of the line to its projected point on the plane. This distance is known as the projection length.

5. Can a line be projected onto any type of plane?

Yes, a line can be projected onto any type of plane. This includes flat planes, curved surfaces, and even 3D objects. However, the method of projection may vary depending on the type of plane.

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