With respect to a fixed origin 0, the lines I, and I,are given by the equations l_{1}: \mathbf{r}=\left(\begin{array}{r} 5 \\ -3 \\ p \end{array}\right)+\lambda\left(\begin{array}{r} 0 \\ 1 \\ -3 \end{array}\right),

\quad l_{2}: \mathbf{r}=\left(\begin{array}{r} 8 \\ 5 \\ -2 \end{array}\right)+\mu\left(\begin{array}{r} 3 \\ 4 \\ -5 \end{array}\right) where 2 and µ are scalar parameters and p is a constant. The lines l1, and l2, intersect at the point A. (a) Find the coordinates of A. (b) Find the value of the constant p. (c) Find the acute angle between l1, and l2,, giving your answer in degrees to 2 decimal places. The point B lies on l2, where µ = 1 (d) Find the shortest distance from the point B to the line 1,, giving your answer to 3 significant figures.