Be able to use vectors in two dimensions.

i.e. Learners should be able to use vectors expressed as \(x\bold{i} + y\bold{j}\) or as a column vector \(\begin{pmatrix} x \\ y \end{pmatrix}\), to use vector notation appropriately either as \(\overrightarrow{AB}\) or \(\bold{a}\).

Learners should know the difference between a scalar and a vector, and should distinguish between them carefully when writing by hand.

Vectors in 2D and 3D

Be able to use vectors in three dimensions.

i.e. Learners should be able to use vectors expressed as \(x\bold{i} + y\bold{j} + z\bold{k}\) or as a column vector \(\begin{pmatrix} x \\ y \\ z \end{pmatrix}\).

Includes extending 1.10c to 1.10g to include vectors in three dimensions, excluding the direction of a vector in three dimensions.

Vectors in 2D and 3D

Be able to calculate the magnitude and direction of a vector and convert between component form and magnitude/direction form.

Learners should know that the modulus of a vector is its magnitude and the direction of a vector is given by the angle the vector makes with a horizontal line parallel to the positive x-axis. The direction of a vector will be taken to be in the interval \([0°,360°).

Includes use of the notation \(|\bold{a}|\) for the magnitude of \(\bold{a}\) and \(|\overrightarrow{OA}|\) for the magnitude of \(\overrightarrow{OA}\).

Learners should be able to calculate the magnitude of a vector \(\begin{pmatrix} x \\ y \end{pmatrix}\) as \(\sqrt{x^2+y^2}\) and its direction by using \(\tan^{-1}{\Bigg(\dfrac{x}{y}\Bigg)}\).

Magnitude and direction of a vector

Be able to add vectors diagrammatically and perform the algebraic operations of vector addition and multiplication by scalars, and understand their geometrical interpretations.

i.e. Either a scaling of a single vector or a displacement from one position to another by adding one or more vectors, often in the form of a triangle of vectors.

Vector addition and multiplication by a scalar

Understand and be able to use position vectors.

Learners should understand the meaning of displacement vector, component vector, resultant vector, parallel vector, equal vector and unit vector.

Position vectors

Be able to calculate the distance between two points represented by position vectors.

i.e. The distance between the points \(a\bold{i} + b\bold{j}\) and \(c\bold{i} + d\bold{j}\) is \(\sqrt{(c-a)^2 + (d-b)^2}\).

Position vectors

Be able to use vectors to solve problems in pure mathematics and in context, including forces.

Solve problems using vectors

Be able to use vectors to solve problems in kinematics.

e.g. The equations of uniform acceleration may be used in vector form to find an unknown. See section 3.02e.

Solve problems using vectors