IB+Standard+Level+-+Vectors

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The vectors topic has remained unchanged in the new syllabus

5.1

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.

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**//.

The angle between two lines.

5.4

Distinguishing between coincident and parallel lines.

Finding the point of intersection of two lines.


 * Determining whether two lines intersect.**

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