Last updated on Sep 23, 2026

Magnitude & Direction (Edexcel A-Level Mathematics): Quizzes

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Magnitude & Direction

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What is the formula for the magnitude of a 2D vector $\mathbf{a} = \begin{pmatrix} a_1 \\ a_2 \end{pmatrix}$ ?

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

For a 3D vector $\mathbf{a} = \begin{pmatrix} a_1 \\ a_2 \\ a_3 \end{pmatrix}$ , what is $|\mathbf{a}|$ ?

$\sqrt{a_1^2 + a_2^2 + a_3^2}$

What is the magnitude of the vector $\begin{pmatrix} 2 \\ 3 \end{pmatrix}$ ?

$\sqrt{13}$

Find $|\mathbf{x}|$ when $\mathbf{x} = \begin{pmatrix} -2 \\ -4 \end{pmatrix}$ .

$2\sqrt{5}$

What formula gives the direction angle $\theta$ of a 2D vector with components $a_1, a_2$ ?

$\theta = \tan^{-1}\left(\frac{a_2}{a_1}\right)$

What is the direction of $\begin{pmatrix} 3 \\ 2 \end{pmatrix}$ (to 1 d.p.)?

$33.7°$

What does the notation $|\mathbf{a}|$ represent?

The magnitude of vector $\mathbf{a}$

For $\begin{pmatrix} -4 \\ -2 \end{pmatrix}$ in the second quadrant, the direction is approximately:

$207°$

A vector has magnitude $3$ and direction $120°$ . What is its $x$ -component?

$-\frac{3}{2}$

A vector has magnitude $3$ and direction $120°$ . What is its $y$ -component?

$\frac{3\sqrt{3}}{2}$

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