Referred to a fixed origin [math]O[/math], the points [math]A[/math]and [math]B[/math]have position vectors [math]\left(\begin{matrix}\begin{matrix}\begin{matrix}1\\2\\-3\end{matrix}\end{matrix}\end{matrix}\right)[/math]and [math]\left(\begin{matrix}5\\0\\-3\end{matrix}\right)[/math] respectively.[br]a) Find, in vector form, an equation of the line [math]l_1[/math], which passes through [math]A[/math]and [math]B[/math]. (3 marks)[br]The line [math]l_2[/math]has equation [math]r=\left(\begin{matrix}4\\-4\\3\end{matrix}\right)+\mu\left(\begin{matrix}1\\-2\\2\end{matrix}\right)[/math], where [math]\mu[/math] is a scalar parameter.[br]b) Show that [math]A[/math] lies on [math]l_2[/math]. (2 marks)[br]c) Find, in degrees, the acute angle between the lines [math]l_1[/math]and [math]l_2[/math]. (4 marks)[br]The point [math]C[/math] with position vector [math]\left(\begin{matrix}0\\4\\-5\end{matrix}\right)[/math] lies on [math]l_2[/math].[br]d) Find the shortest distance from [math]C[/math]to the line [math]l_1[/math]. (4 marks)