## Exam-Style Question on Vectors## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 48. This question is similar to one that appeared on an IB Standard paper in 2014. The use of a calculator is not allowed.

The line \(L_1\) passes through the points A(3, 5, 1) and B(3, 6, 0).

(a) Show that \(AB=\begin{pmatrix} 0 \\ 1 \\ -1 \\ \end{pmatrix}\)

(b) Find a direction vector for \(L_1\)

(c) a vector equation for \(L_1\)

Another line \(L_2\) has equation \(\begin{pmatrix} 8 \\ 3 \\ -2 \\ \end{pmatrix} + t \begin{pmatrix} -1 \\ 1 \\ 0 \\ \end{pmatrix}\). The lines \(L_1\) and \(L_2\) intersect at the point P.

(d) Find the coordinates of P.

(e) Find a direction vector for \(L_2\).

(f) Hence, find the angle between \(L_1\) and \(L_2\).

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