3. Geometry and Trigonometry

Vector Equations Of Lines — Quiz

Test your understanding of vector equations of lines with 5 practice questions.

Practice Questions

Question 1

Which vector equation represents a line passing through the point $\begin{pmatrix}1\\2\end{pmatrix}$ with direction vector $\begin{pmatrix}3\\-1\end{pmatrix}$?

Question 2

In the vector equation $\mathbf{r}=\begin{pmatrix}2\\-1\end{pmatrix}+t\begin{pmatrix}4\\3\end{pmatrix}$, what is the direction vector of the line?

Question 3

Which point lies on the line $\mathbf{r}=\begin{pmatrix}0\\5\end{pmatrix}+t\begin{pmatrix}2\\-1\end{pmatrix}$ when $t=3$?

Question 4

The line $\mathbf{r}=\begin{pmatrix}1\\4\end{pmatrix}+t\begin{pmatrix}2\\6\end{pmatrix}$ can also be written in the form $y=mx+c$. What is the gradient $m$?

Question 5

Which vector equation describes the same line as the parametric equations $x=5-2t$ and $y=1+t$?