Intersection points of the planes

Thread starter abs123456
Start date May 18, 2011
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Intersection Planes Points

In summary, intersection points of planes refer to the points where two or more planes intersect in space. These points can be found using algebraic methods or by graphing the planes. Two planes can only intersect at one point, and if they do not intersect, it means they are parallel. Intersection points of planes have practical applications in fields such as architecture, engineering, and aviation. They are used to determine angles and relationships between surfaces and in flight planning.

May 18, 2011

abs123456

Homework Statement

Find all the intersection points of the planes:
2x-y-z=3
x+2y+3z= 7

Homework Equations

Whats the best n most simplest way to go about this question. Thanks

The Attempt at a Solution

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May 18, 2011

tiny-tim

Science Advisor

Homework Helper

hi abs123456!

abs123456 said:

Whats the best n most simplest way to go about this question.

well, it's a line, so find the direction of the line first

FAQ: Intersection points of the planes

What are intersection points of the planes?

Intersection points of the planes refer to the points where two or more planes intersect or overlap in space. These points are important in geometry and can be used to determine equations and relationships between different planes.

How do you find the intersection points of two planes?

To find the intersection points of two planes, you can use algebraic methods such as substitution or elimination. This involves setting the equations of the planes equal to each other and solving for the variables. Another method is to graph the planes and visually determine the intersection points.

Can two planes intersect at more than one point?

No, two planes in three-dimensional space can only intersect at one point. This is because two distinct lines can only intersect at one point, and planes are made up of infinitely many lines.

What does it mean when two planes do not intersect?

If two planes do not intersect, it means that they are parallel to each other. This means that the planes lie in the same direction and will never intersect or overlap in space.

How are intersection points of planes used in real life?

Intersection points of planes have many real-life applications, such as in architecture, engineering, and aviation. They are used to determine the angles and relationships between different surfaces, and to create 3D models of structures. In aviation, intersection points of planes are used in navigation and flight planning.