A-Level Maths OCR B (MEI) H640

Understand the language of vectors in two dimensions.

Scalar, vector, modulus, magnitude, direction, position vector, unit vector, cartesian components, equal vectors, parallel vectors, collinear.

Notation:

• Vectors printed in bold.
• Unit vectors $\bold{i}$, $\bold{j}$, $\bold{\hat{r}}$
• The magnitude of the vector $\bold{a}$ is written $|\bold{a}|$ or $a$.
• $\bold{a} = \begin{pmatrix} a_1 \\ a_2 \end{pmatrix}$

Be able to add and subtract vectors using a diagram or algebraically, multiply a vector by a scalar, and express a vector as a combination of others.

Geometrical interpretation. Includes general vectors not expressed in component form.

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

Notation:

• Magnitude-direction

Understand and use position vectors.

Including interpreting components of a position vector as the Cartesian coordinates of the point.

$\overrightarrow{AB} = \bold{b} - \bold{a}$

Notation:

• $\overrightarrow{OB}$ or $\bold{b}$
• $\bold{r} = \begin{pmatrix} x \\ y \end{pmatrix}$

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

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

Includes interpreting the sum of vectors representing forces as the resultant force.

Understand the language of vectors in three dimensions.

Extend the work of 11.2 to 11.6 to include vectors in three dimensions.

Notation:

• Unit vectors $\bold{i}$, $\bold{j}$, $\bold{k}$, $\bold{\hat{r}}$
• $\bold{a} = \begin{pmatrix} a_1 \\ a_2 \\ a_3 \end{pmatrix}$