2023TrialShort answer

Q13 (d) (i)

2 marks

Question

Consider the line $\ell_1$ joining

\begin{pmatrix}-3\\-1\\4\end{pmatrix} \quad\text{and}\quad \begin{pmatrix}-1\\0\\3\end{pmatrix}.

Determine the vector equation of $\ell_1$ .

Try the question before revealing the answer.

Solution

\begin{aligned} \begin{pmatrix}-1\\0\\3\end{pmatrix}-\begin{pmatrix}-3\\-1\\4\end{pmatrix} &=\begin{pmatrix}2\\1\\-1\end{pmatrix}\\ \therefore\ell_1:\quad \vec r&=\begin{pmatrix}-1\\0\\3\end{pmatrix}+\lambda\begin{pmatrix}2\\1\\-1\end{pmatrix},\quad \lambda\in\mathbb R \end{aligned}

Alternative shown:

\vec r=\begin{pmatrix}-3\\-1\\4\end{pmatrix}+\lambda\begin{pmatrix}2\\1\\-1\end{pmatrix},\quad \lambda\in\mathbb R

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Syllabus alignment

Vectors

Vectors and vector equations of linesUse coordinates and vector equations for curves, lines, line segments and spheres in two and three dimensions.
Introduction to three-dimensional vectorsRepresent and operate with vectors in three dimensions using unit, component, ordered-triple and column-vector forms.

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