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

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Vectors in 3 Dimensions
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What is the magnitude of vector a=(xyz)\mathbf{a} = \begin{pmatrix} x \\ y \\ z \end{pmatrix}?

x2+y2+z2\sqrt{x^2 + y^2 + z^2}

What is a unit vector?

A vector of length 1

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

Divide a\mathbf{a} by its magnitude

How do you find AB→\overrightarrow{AB} from position vectors A\mathbf{A} and B\mathbf{B}?

B−A\mathbf{B} - \mathbf{A}

What is ∣a∣|\mathbf{a}| if a=(614)\mathbf{a} = \begin{pmatrix} 6 \\ 1 \\ 4 \end{pmatrix}?

53\sqrt{53}

Find distance between A=(231)\mathbf{A} = \begin{pmatrix} 2 \\ 3 \\ 1 \end{pmatrix} and B=(−263)\mathbf{B} = \begin{pmatrix} -2 \\ 6 \\ 3 \end{pmatrix}.

29\sqrt{29}

In 3D, what does it mean for two vectors to be parallel?

One is a multiple of the other

If (λ−2λμ)\begin{pmatrix} \lambda \\ -2\lambda \\ \mu \end{pmatrix} is parallel to (2−4−3)\begin{pmatrix} 2 \\ -4 \\ -3 \end{pmatrix}, what equation holds?

3λ+2μ=03\lambda + 2\mu = 0

If (λ−2λμ)\begin{pmatrix} \lambda \\ -2\lambda \\ \mu \end{pmatrix} has ∣ξ∣=229|\mathbf{\xi}| = 2\sqrt{29} and 3λ+2μ=03\lambda + 2\mu = 0, what is λ\lambda?

±4\pm 4

What is ∣AB→∣|\overrightarrow{AB}| if AB→=(−432)\overrightarrow{AB} = \begin{pmatrix} -4 \\ 3 \\ 2 \end{pmatrix}?

29\sqrt{29}

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