Modelling involving Numerical Methods (AQA A-Level Mathematics): Flashcards

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Basic Vectors
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What two properties do vectors possess?

Magnitude (size) and direction

Magnitude of a=(a1a2)\mathbf{a} = \begin{pmatrix} a_1 \\ a_2 \end{pmatrix}

a=a12+a22|\mathbf{a}| = \sqrt{a_1^2 + a_2^2}

Method for adding vectors

Component-wise: add corresponding components

Scalar multiplication effect on direction

Does not change direction

Position vector definition

Vector from origin to a point

Displacement vector definition

Vector between any two points

Formula for AB\overrightarrow{AB}

BAB - A

Unit vector definition

Vector with magnitude of 1 unit

How to find unit vector from a\mathbf{a}

Divide a\mathbf{a} by its magnitude

Scalar multiplication effect on magnitude

Changes the magnitude

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