7.4 Lines and Planes in 3D Space: Equations and Diagrams
In the previous section, you learned how to say some mathematical symbols used in lines and planes in 3D space. Now, you will practise reading out full equations and labelling diagrams. This will help you use mathematical language in real examples. By practising these skills, you will become more confident when speaking about mathematics in lectures, explaining your work to others, and understanding what your lecturers and classmates say during lectures, seminars, and tutorials.
In this first activity, you will practise reading out some equations. This will help you improve your pronunciation and become more confident when talking about mathematics.
For each equation, first take a moment to consider how you would say it, then try reading it out loud. After reading each equation aloud, select the 'Answer' button below the equation to see the correct phrasing, and use the 'Play' button to listen to the recording.
You can also do this activity with a partner or in a small group. Working together lets you take turns, help each other, and share what you know about reading mathematics in English.
How would you read out the equations below?
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- [latex](x, y, z) = (1, 2, -1) + s(1, -1, 2)[/latex]
Answer
x, y, z is equal to one two minus one plus, s times, one minus one two.
- [latex](x, y, z) = (1, 2, -1) + s(1, -1, 2)[/latex]
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- [latex]\text{proj}_\textbf{v} (\textbf{u}) = \left( \frac {\textbf{u} \cdot \textbf{v}} {|\textbf{v}|^2}\right) \textbf{v}[/latex]
Answer
the projection of u along v is equal to, u dot v over the magnitude of v squared, times v.
- [latex]\text{proj}_\textbf{v} (\textbf{u}) = \left( \frac {\textbf{u} \cdot \textbf{v}} {|\textbf{v}|^2}\right) \textbf{v}[/latex]
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- [latex]2 x- y + z = 2 \cdot 2 -1 + 3 = 6[/latex]
Answer
two x minus y plus z is equal to, two times two minus one plus three, which is equal to six.
- [latex]2 x- y + z = 2 \cdot 2 -1 + 3 = 6[/latex]
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- [latex]\text{proj}_\textbf{v} (\textbf{u}) = \alpha \textbf{v}[/latex]
Answer
the projection of u in the direction of v is equal to alpha v.
- [latex]\text{proj}_\textbf{v} (\textbf{u}) = \alpha \textbf{v}[/latex]
In this second activity, you will do the opposite of the previous activity. Before, you saw a mathematical equation and said it in English. Now, you will read and listen to the English 'read-out' by pressing the 'Audio' button, and then write down the correct mathematical equation. After writing down the equation, select the ‘Turn’ button to reveal the correct answer, then select the ‘Next’ button to proceed.
For example, if you hear or read A squared plus B squared is equal to C squared, you should write [latex]A^2+B^2=C^2[/latex].
This activity will help you practise turning English sentences into mathematical symbols. It will also improve your listening, reading, and writing skills in mathematics, making it easier to understand and communicate mathematical ideas.
