I. Vectors, straight lines, circles Point The lenght of a line segment Coordinates of the center of a line segment Vector Vector – origin at point A and.

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Presentation transcript:

I. Vectors, straight lines, circles Point The lenght of a line segment Coordinates of the center of a line segment Vector Vector – origin at point A and the end at point B Zero vector An opposite vector with respect to vector v The lenght of a vector

The sum of two vectors, The product of a number and a vector The scalar product of vectors, The vectorial product, Geometrical scalar and vectorial products:

Equations of a straight line: ■■ ■ General Segmental Directional Determinant Parametrical Two - points Vector perpendicular to the straight line Vector parallel to the straight line

δ, the distance between point P(x 0,y 0 ) and the straight line φ, the angle between two straight lines The condition of perpendicularity The condition of parallelity

1. Write an equation of a straight line, perpendicular to the line x + 3y – 7 = 0, passing through the point A=(a;b), where a and b are roots of the equation: 2. Draw a line through the point A=(a;b), which is perpendicular to the line x + 2y – 5 = 0, where a is the solution of the equation: and b is the solution of the equation:

3. There are two straight lines k and l of equations k : 3x – y = –18 l : x + y = 2 and the point A=(3;–1). Find such a point P on OX axis, so that vectors are perpendicular, giving that point B is a common point of lines k and l. 4.Points A=(1;2); B=(–1;–1); C=(5;2) are vertexes of a triangle. a) Write an equation of a straight line which contains the triangle’s height from the vertex A. b) Determinate point’s D coordinates, so that the tetragon ABCD is a parallelogram.

SET OF PROBLEMS 1. Take into account the following sets: Determine: 2. The third term of an arithmetic sequence is equal to the sixth term is equal toDetermine this sequence. How many initial terms one needs to take, so that their sum is 14650

3. It is given the polynomial The roots of the polynomial are numbers: –1; p; q. Determine coefficients a; b; c of W (x), if p is the solution of the equation and 4. The straight line of the equation y + 3x + 2 = 0 intersects the parabola in points A and B. a) Calculate the area and the circumference of the triangle ABS, where S is the vertex of the parabola. b) Write down a circle’s equation which is circumscribed on this triangle.