#11.1
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 \(a\).
\(\bold{a} = \begin{pmatrix} a_1 \\ a_2 \end{pmatrix}\)
#11.2
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.
#11.3
Be able to calculate the magnitude and direction of a vector and convert between component form and magnitude-direction form.
Notation: Magnitude-direction
#11.4
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 \(\bold{b}\)
\(\bold{r} = \begin{pmatrix} x \\ y \end{pmatrix}\)
#11.5
Be able to calculate the distance between two points represented by position vectors.
#11.6
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.
#11.7
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 \(\bold{i}\), \(\bold{j}\), \(\bold{k}\), \(\bold{\hat{r}}\)
\(\bold{a} = \begin{pmatrix} a_1 \\ a_2 \\ a_3 \end{pmatrix}\)