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11th Grade - Geometry

11th Grade lesson

8 - Geometry


The notions about the vectors of the plane are also true in space. Two collinear vectors share the same direction (there is a number k such as one vector is k times the other), and two vectors are orthogonal if their scalar product is zero.


Equation of a line (d) in space

line equation

To determine the equation of a line in space that has direction vector vector and that passes through coordinates of a point, note that this line (d) is the set of points coordinates such that
math equation and math equation

are collinear. vector and vector are collinear if there is a number k such that colinear vectors, so
math equation then parametric equation of a line
The last system is called a parametric equation of the line (d).


Equation of a plane P in space

plan is a normal vector to a plane P, point plan a point in this plane, and A the orthogonal projection of M on P. The vectors vector math and vector math are orthogonal.
math equation

Thus if a point point math belongs to the plane P, there is a number d such as math equation. The last equality is the equation of a plane. When you have this kind of equation for a plane (cartesian equation), you can give the coordinates of a normal vector to the plane. Read the coefficients before x, y and z.


See also : geometry on fmaths.com



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11th Grade Geometry

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