IB+Higher+Level+-+Vectors

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The vectors topic has remained largely unchanged in the new syllabus

5.1


 * Concept of a vector.**


 * Representation of vectors using directed line segments.**


 * Unit vectors; base vactors //i,j,k.//**

Vectors as displacements in the plane and in three dimensions.

Components of a vector; column representation;


 * v =** (v// 1 //,v// 2 //,v// 3 //) = v// 1 //**i** + v// 2 //**j** + v// 3 //**k**.

Algebraic and geometric approaches to the following
 * the sum and difference of two vectors; the zero vector, the vector //**-v**//;
 * multiplication by a scalar, //k**v**// ; parallel vectors;
 * magnitude of a vector, |//**v**//| ;
 * unit vectors; base vectors; //**i**//,//**j**// and //**k**//;
 * position vectors OA = //**a;**//
 * **AB = OB - OA = //b - a//.**

5.2

The scalar product of two vectors. //**v.w** = |v||w|cos// 0 //; **v.w** = v 1 ////w 1 + v// 2 //w// 2 //+ v// 3 //w// 3 //.//

Algebraic properties of the scalar product.

Perpendicular vectors; parallel vectors.

The angle between two vectors.

5.3

Vector equation of a line in two and three dimensions: //**r** = **a** + t**b**//.


 * Simple applications to kinematics**

The angle between two lines.

5.4

Coincident, parallel, intersecting and skew lines, distinguishing between these cases.

Points of intersection.

5.5

The vector product of two vectors, **//v//**//x//**//w.//**


 * Properties of the vector product.**

The determinant representation.

Geometric interpretation of |//**v**x**w**//| //**.**//

5.6

Vector equation of a plane **r //= a +//** //t//**//b +//** //u//**//c .//**

Use of normal vector to obtain the form **//r.n = a.n//**.

Cartesian equation of a plane //ax + by + cz = d//

5.7

Intersections of: a line with a plane; two planes; three planes.

Angle between: a line and a plane; two planes.

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