CAIE A-Level Mathematics A2 3.7.4 Straight Lines Questions

Practise vector equations of straight lines and geometric relationships in three dimensions.

Exam points

write vector equations for straight lines
find intersections, parallelism and relationships between lines
solve three-dimensional geometry problems using line vectors

[Maximum number: 3]

With respect to the origin O, the position vectors of the points A and B are given by $\overrightarrow{O A}=\left(\begin{array}{r}1 \\ 2 \\ -1\end{array}\right)$ and $\overrightarrow{O B}=\left(\begin{array}{l}0 \\ 3 \\ 1\end{array}\right)$ .

Find a vector equation for the line l through A and B.

Obtain direction vector -i+j+2 k, or equivalent
Accept answers as column vectors throughout.
Use a correct method to form a vector equation
State answer $\mathbf{r}=\mathbf{i}+2 \mathbf{j}-\mathbf{k}+\lambda(-\mathbf{i}+\mathbf{j}+2 \mathbf{k})$ , or equivalent correct form
e.g. $\mathbf{r}=\left(\begin{array}{l}0 1\end{array}\right)+\mu\left(\begin{array}{c}1 -1 -2\end{array}\right)$ Allow $\left(\begin{array}{l}x y z\end{array}\right)$ for r.

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CAIE A-Level Mathematics A2 3.7.4 Straight Lines Questions question 1