The line ${{l}_{2}}$ passes through $A\left( 3,1,-2 \right)$ and is parallel to the direction vector

Question

The line ${{l}_{2}}$ passes through $A\left( 3,1,-2 ight)$ and is parallel to the direction vector $\left( \begin{matrix}7 \15 \1 \\end{matrix} ight)$. ${{l}_{2}}$ intersects ${{l}_{1}}:\mathbf{r}=\left( \begin{matrix} -12 \ -22 \ 11 \\end{matrix} ight)+\lambda \left( \begin{matrix}4 \ 4 \ -7 \\end{matrix} ight);\lambda \in \mathbb{R}$ at $C$.Find the coordinates of $C$, the acute angle between ${{l}_{1}}$ and ${{l}_{2}}$, the vector line equation of mirror image of ${{l}_{2}}$ in ${{l}_{1}}$.

Accepted Answer

(i) $C(-4, -14, -3)$ (ii) $57.1^{\circ}$ (iii) $\mathbf{r} = \begin{pmatrix} -4 \\ -14 \\ -3 \end{pmatrix} + \alpha \begin{pmatrix} -1 \\ 7 \\ 15 \end{pmatrix}$

Unit 13.2 Worked Example 2

Unit 13.2 Worked Example 2

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