# Exam Style Question

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

### Vectors

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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