Addition and subtraction of vectors, multiplication of vectors by numbers. Properties of these operations, apllications to geometric problems. Center of masses of a system of points. Cartesian coordinates of a vector. Their behavior under the linear operations.
Dot product of vectors and its properties. Calculation of dot product in coordinates. Condition for orthogonality of vectors. Geometric applications.
Cross product of vectors in the 3-space. Algebraic properties. Formula in coordinates.
Various forms of equation for a line on the plane. Radius-vector of a point. Equation of a line on the plane in the vector form. The formula for the distance from a point to a line. Equations for a plane in the 3-space. Equations for a line in the 3-space. Formulas for the distance between skew lines.
Plane curves of degree 2. The simplest equations. Conic sections. Foci and dirctrix. Surfaces of degree 2 in the 3-space.
Area of plane figures: the main properties and calculation for polygons. Relation to the cross product. Area of a disk. Relation to the integrals. Volume of geometric figures in the 3-space. Volumes of elementary polyhedra. Volume of a ball.
Students with Disabilities: If you have a physical, psychological, medical, or learning disability that may impact on your ability to carry out assigned course work, you are strongly urged to contact the staff in the Disabled Student Services (DSS) office: Room 133 in the Humanities Building; 632-6748v/TDD. The DSS office will review your concerns and determine, with you, what accommodations are necessary and appropriate. A written DSS recommendation should be brought to your lecturer who will make a decision on what special arrangements will be made. All information and documentation of disability is confidential. Arrangements should be made early in the semester so that your needs can be accommodated.