Pure Mathematics
Statistics

Unit 13.2 Worked Example 4

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].

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