Last updated on Sep 22, 2026

Vectors in 3 Dimensions (AQA A-Level Mathematics): Quizzes

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Vectors in 3 Dimensions

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What is the magnitude of vector $\mathbf{a} = \begin{pmatrix} 3 \\ 4 \\ 12 \end{pmatrix}$ ?

$13$

What is the length of a unit vector?

$1$

How do you find a unit vector parallel to $\mathbf{a}$ ?

Divide $\mathbf{a}$ by $|\mathbf{a}|$

If two vectors in 3D are parallel, what is their relationship?

One is a multiple of the other

What is $|\mathbf{v}|$ if $\mathbf{v} = \begin{pmatrix} 2 \\ -3 \\ 6 \end{pmatrix}$ ?

$7$

If $\mathbf{\xi} = \begin{pmatrix} k \\ -2k \\ m \end{pmatrix}$ is parallel to $\begin{pmatrix} 2 \\ -4 \\ -3 \end{pmatrix}$ , find the relation.

$3k + 2m = 0$

Find distance between $\mathbf{A} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}$ and $\mathbf{B} = \begin{pmatrix} 4 \\ 6 \\ 3 \end{pmatrix}$ .

$5$

What do we discuss in 3D instead of gradients?

Directions

If $|\mathbf{w}| = \sqrt{5\lambda^2 + \mu^2} = 2\sqrt{29}$ , what is $5\lambda^2 + \mu^2$ ?

$116$

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