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

Exam questions on 3.11 Vector equation of a line

1. 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
2. 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
3. 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