When an infinite amount of points extends in only two directions, we call it a line. A line has only one dimension and that is the length. However, a plane is something close to a line. A plane is a two-dimensional surface and like a line, it extends up to infinity. Usually, we talk about the line-line intersection. It means that two or more than two lines meet at a point or points, we call those point/points intersection point/points. The same concept is of a line-plane intersection. It means that when a line and plane comes in contact with each other. That point will be known as a line-plane intersection. Show
Line-plane and line-line are not the only intersections in geometry, you will also find line-point intersection as well. There is one problem, how can you identify whether the intersection is a line-line, line-point, or no intersection without the help of the graph? Well, there is one method through which you can find the type of intersection. You can find it with the help of the ranks. Line Defined by Two PlanesThe lines are  Form a system with equations in order to calculate the ranks. The next step is to calculate the coefficient matrix and augmented matrix and compare the values with values of different types of intersection. Here The relationship between the line and the plane can be described as follows: Point IntersectionThe basic condition for the intersecting line is that both lines should cut each other on a single point. The identification of intersecting lines is that the rank of the matrix will always be equal to the rank of the augmented matrix and they both should be equal to 3 i.e. No IntersectionWhen two or more than two lines don't meet each other (or cut each other) that means you have a case of no intersection. The rank of the coefficient matrix will always be equal to Line IntersectionImagine a line and then draw another line which is overlapping the first line. In this case, at every point, there will be an intersecting point. The result will be that there will be an infinite number of intersection points, therefore, we will say that there will be an infinite number of intersecting points. This type of intersection is called line intersection and lines are called coincident lines. At this point, you might be wondering what is the difference between intersecting lines and coincident lines, the only difference is that the intersecting line will always intersect at a single point, however, coincident lines intersect at many points that we make it equal to infinity. Furthermore, the coefficient rank of coincident lines will be Parallel LinesParallel lines mean both lines have a constant distance and they don't meet. Draw a line of The best Maths tutors available 5 (27 reviews) Akash £20 /h 1st lesson free! 4.9 (40 reviews) Intasar £49 /h 1st lesson free! 5 (30 reviews) Daniel £60 /h 1st lesson free! 4.9 (139 reviews) Harjinder £25 /h 1st lesson free! 4.9 (36 reviews) Sehaj £35 /h 1st lesson free! 5 (29 reviews) Ollie £35 /h 1st lesson free! 5 (23 reviews) Johann £25 /h 1st lesson free! 5 (36 reviews) Ritchard £85 /h 1st lesson free! 5 (27 reviews) Akash £20 /h 1st lesson free! 4.9 (40 reviews) Intasar £49 /h 1st lesson free! 5 (30 reviews) Daniel £60 /h 1st lesson free! 4.9 (139 reviews) Harjinder £25 /h 1st lesson free! 4.9 (36 reviews) Sehaj £35 /h 1st lesson free! 5 (29 reviews) Ollie £35 /h 1st lesson free! 5 (23 reviews) Johann £25 /h 1st lesson free! 5 (36 reviews) Ritchard £85 /h 1st lesson free! Let's go ExamplesState the relationship between the line and the plane: 1. Form the system of equations. Find the rank of the coefficient matrix. Determine the rank of the augmented matrix. Compare the ranks. Point intersection.
2. Determine the rank of the augmented matrix. Compare the ranks. The line and plane are parallel.
The Line is Defined by a Point and a VectorThe line is defined by Point A, the vector, The platform that connects tutors and students First Lesson Free Did you like this article? Rate it! 4.00 (3 rating(s)) Emma I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places. What would be the intersection of a plane and a line?If a line and a plane intersect one another, the intersection will be a single point, or a line (if the line lies in the plane). If we want to double-check ourselves, we can plug this coordinate point back into the equation of the plane.
What is the intersection of a plane and a line perpendicular?A line is perpendicular to a plane when it extends directly away from it, like a pencil standing up on a table. It can't point anywhere else but directly away from the table. When a line is perpendicular to two lines on the plane (where they intersect), it is perpendicular to the plane.
Do a plane and a line always intersect?A given line and a given plane may or may not intersect. If the line does intersect with the plane, it's possible that the line is completely contained in the plane as well.
What is the intersection of a plane called?Answer and Explanation:
The intersection of two planes is called a line. Planes are two-dimensional flat surfaces.
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What is the intersection between a plane and a line?
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