![]() CATEGORIES: BiologyChemistryConstructionCultureEcologyEconomyElectronicsFinanceGeographyHistoryInformaticsLawMathematicsMechanicsMedicineOtherPedagogyPhilosophyPhysicsPolicyPsychologySociologySportTourism |
Analytic geometry in space. Vectors. Simple operations with vectors. The scalar, vector and mixed product of vectors
LECTURE PLAN
1. Planes 2. Vectors. Operations with vectors.
Planes
The general equation of a plane. Suppose given a vector It is required to write an equation of the plane.
M(x,y,z) M0(x0,y0,z0)
According to the general scheme, we take an arbitrary point M(x,y,z) in the plane. Consider the vector Since
Denoting this numerical expression by D, we obtain
This is the general equation of a plane; the coefficients of A,B and C of x, y, and z are the coordinates of the normal vector
The three-intercept equation of a plane. Suppose given a plane not passing through the origin but intersecting the coordinate axes at points
The coefficients are not known yet, so we choose them so, that the plane cuts out the given segments a,b, and c on the coordinate axes. Date: 2015-01-02; view: 1478
|