Here are vector equations of three lines.
\(\mathbf{a}=\begin{pmatrix}4\\0\\-2\end{pmatrix}+\alpha\begin{pmatrix}-1\\1\\4\end{pmatrix}\)
\(\mathbf{b}=\begin{pmatrix}1\\3\\10\end{pmatrix}+\beta\begin{pmatrix}-2\\-1\\2\end{pmatrix}\)
\(\mathbf{c}=\begin{pmatrix}2\\-1\\0\end{pmatrix}+\gamma\begin{pmatrix}1\\2\\2\end{pmatrix}\)
Before doing any calculations,
- try to visualise the lines in 3D space. What can you say about them?
- do you think any of them might be parallel or perpendicular?
- might they intersect?
Now check your predictions and work out what geometrical shape or pattern the lines make.
