The line ${{l}_{3}}$ which passes through $B\left( 7,4,-5 \right)$ and is parallel to the direction

Question

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

Accepted Answer

(i) $\left(\displaystyle\frac{57}{11}, \frac{24}{11}, -\frac{20}{11}\right)$; (ii) $40.8^\circ$; (iii) $\mathbf{r} = \displaystyle\frac{1}{11}\begin{pmatrix} 57 \\ 24 \\ -20 \end{pmatrix} + t\begin{pmatrix} 50 \\ -38 \\ -5 \end{pmatrix}$

Unit 13.2 Worked Example 4

Unit 13.2 Worked Example 4

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