IB Maths AA 3.12 Definitions

This page contains our IB Maths AA definitions for 3.12. By learning each one of these definitions, you will fully cover the content for IB Maths AA 'Planes'.

All Topic 3 Sub-topics 3.1: Fundamentals Of Geometry 3.2: Introduction To Trigonometry 3.3: Applied Trigonometry 3.4: Circles 3.5: Unit Circle 3.6: Trigonometric Identities 3.7: Trigonometric Graphs (HL)3.8: Advanced trigonometry (HL)3.9: Compound angles (HL)3.10: Vectors (HL)3.11: Lines (HL)3.12: Planes

Cartesian equation

An equation in

x

y

, and

z

that describes a plane in the form

ax+by+cz=d

, where

(a,b,c)

is perpendicular to the plane.

direction vector

A non-zero vector parallel to a line that gives its direction; in $r=a+\lambda b$ , $b$ determines how $r$ changes as $\lambda$ changes.

parametric equation

A representation of a line or plane using one or more parameters, so that varying the parameter values generates all points on the object.

plane

A two-dimensional coordinate system used to represent complex numbers, with the horizontal axis as the real axis and the vertical axis as the imaginary axis.

solution sets

The collection of all points that satisfy given equations, interpreted geometrically as an intersection point, a line of points, no common points, or infinitely many points.

vector equation

A representation of a line in 2D or 3D written as a position vector $\textbf{r}$ in terms of a fixed point and a scalar parameter, typically in the form $r = a + \lambda b$ .

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