The line [latex]{{l}_{3}}[/latex] which passes through [latex]B\left( 7,4,-5 \right)[/latex] and is parallel to the direction vector [latex]\left( \begin{matrix}4 \\4 \\-7 \\\end{matrix} \right)[/latex]. The plane [latex]{{p}_{1}}[/latex] has the equation [latex]x-3y+2z=-5[/latex]. Find
(i)
the coordinates of point of intersection between the line [latex]{{l}_{3}}[/latex] and plane [latex]{{p}_{1}}[/latex],
(ii)
the acute angle between the line [latex]{{l}_{3}}[/latex] and plane [latex]{{p}_{1}}[/latex],
(iii)
the equation of line of the image of line [latex]{{l}_{3}}[/latex] in plane [latex]{{p}_{1}}[/latex].