3.11 Vector equation of a lineIB Maths: Applications and Interpretation HL: Flashcards

What these 12 flashcards ask

What is the vector equation of a line?
What does \mathbf{a} represent in \mathbf{r}=\mathbf{a}+\lambda\mathbf{b}?
What does \mathbf{b} represent in \mathbf{r}=\mathbf{a}+\lambda\mathbf{b}?
What is \lambda called?
How do you find a direction vector from two points A and B?
Is the vector equation of a line unique?
How do you test whether a point lies on a line?
What are the parametric equations of \mathbf{r}=\begin{pmatrix}x0 \\ y0 \\ z0\end{pmatrix}+\lambda\begin{pmatrix}l \\ m \\ n\end{pmatrix}?
Convert x=4-2\lambda, y=1+\lambda, z=3\lambda to vector form.
How do you find where a line meets the plane z=0?
In \mathbf{r}=\mathbf{r}0+t\mathbf{v}, what is the speed?
Find a direction vector for the line through (2,5) and (11,-7).

Exam questions on 3.11 Vector equation of a line

A line $l$ has vector equation $\mathbf{r}=\begin{pmatrix}2 \\ -1 \\ 4\end{pmatrix}+\lambda\begin{pmatrix}3 \\ 2 \\ -1\end{pmatrix}$ , where $\lambda\in\mathbb{R}$ .
Find the coordinates of the point where $l$ meets the plane $z=0$ .2 marks
The line $l_1$ passes through the points $A(1,2,-3)$ and $B(4,6,9)$ .
Write down the parametric equations of $l_1$ .2 marks
A lifeboat leaves the harbour at $A(2,5)$ and travels in a straight line through the point $B(11,-7)$ . Coordinates are in km, relative to a lighthouse at the origin $O$ .
Find a vector equation of the line along which the lifeboat travels.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).