Module Identifier MA10110 Module Title COORDINATE AND VECTOR GEOMETRY Academic Year 2001/2002 Co-ordinator Dr V Mavron Semester Semester 1 Other staff Professor T Phillips Pre-Requisite A-level Mathematics or equivalent. Course delivery Lecture 20 x 1 hour lectures Seminars / Tutorials 5 x 1 hour tutorials Workshop 2 x 1 hour workshops (including test) Assessment Continuous assessment 25% Exam 2 Hours (written examination) 75% Resit assessment 2 Hours (written examination) 100%

#### General description

This module introduces some of the fundamental notions of geometry - points, lines, curves, planes and surfaces - analytically, in the language of coordinate geometry. Conics are classified in terms of their equations and geometric properties. The concepts of tangent and normal are developed.

#### Aims

To develop geometric intuition and the ability to view geometric problems analytically and vice versa.

#### Learning outcomes

On completion of this module, a student should be able to:
• identify simple loci analytically and geometrically;
• find equations of angular bisectors and prependiculars;
• determine lengths of tangents to a circle and whether two circles are orthogonal;
• determine equations of coaxial circle systems;
• identify the type of a conic from its equation;
• determine the equations of the tangents and normals to a general conic;
• use vectors to solve elementary problems in geometry;
• express the coordinates of a general point of certain curves parametrically;
• compute scalar and vector products of two vectors;
• compute scalar and vector triple products of three vectors;
• determine the vector equations of lines and planes;
• determine the angle between two planes and the shortest distance from a point to a plane.

#### Syllabus

1. COORDINATE GEOMETRY IN THE REAL PLANE: The straight line. Conics - particular forms and the general form. Identification of centres, foci and major and minor axes. Cases of degeneracy. Changes of axes. The general equation of the tangent. Families of lines and conics. Parametric plane curves. Tangents and the use of derivatives.
2. GEOMETRY IN REAL 3-SPACE: Cartesian coordinates. Equations of lines and planes. The normal. Curves, their tangents and other special direction. Surfaces and their tangent planes. Polar coordinates.
3. INTRODUCTION TO VECTOR METHODS: Unit vectors. Scalar and vector products, angles and orthogonality. Position vectors. Linearly independent vectors. Vector equations of lines and planes.