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danago
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I merged the duplicate thread. This post cannot be deleted!
Integral
Integral
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Points A, B and C have position vectors 3i-j, -i+15j and 9i-25j respectively. Use vectors to prove that A, B and C are collinear.
To prove that points A, B, and C are collinear, you need to show that they lie on the same straight line. This can be done by extending the line segments AB and BC and checking if they intersect at a single point. If they do, then points A, B, and C are collinear.
Proving collinearity between points A, B, and C is important in geometry as it provides information about the relationship between these points. If they are collinear, it means that they lie on the same line, which can help in solving geometric problems and making accurate measurements.
There are several methods for proving collinearity between points A, B, and C. These include the slope method, vector method, and coordinate geometry method. Each method involves different steps and equations, but ultimately they all aim to show that the points lie on the same straight line.
No, points A, B, and C cannot be collinear if they are not on the same line. Collinear points, by definition, must lie on the same straight line. If the points are not on the same line, then they are not collinear.
Yes, proving collinearity between points A, B, and C has many real-world applications. For example, in architecture and construction, proving collinearity can help in accurately determining the placement of structural elements such as beams or columns. In surveying, collinearity can help in creating accurate maps and measurements of land. It is also used in navigation and GPS systems to determine the location of points on a map.