The lines ${{l}_{1}}$ and ${{l}_{2}}$ have equations $\frac{x+8}{2}=\frac{5-y}{2}=z+1$ and $\mathbf{

Question

The lines ${{l}_{1}}$ and ${{l}_{2}}$ have equations $\frac{x+8}{2}=\frac{5-y}{2}=z+1$ and $\mathbf{r}=\alpha \left( \begin{matrix} 6 \ -4 \ 1 \ \end{matrix} ight)$, $\alpha \in \mathbb{R}$ respectively. Find the acute angle between ${{l}_{1}}$ and the $z$-axis. the position vector of the foot of perpendicular, $N$, from the origin to ${{l}_{1}}$. the coordinates of the point of intersection of ${{l}_{1}}$ and ${{l}_{2}}$. Hence, find a vector equation of the reflection of line ${{l}_{2}}$ in the line ${{l}_{1}}$.

Accepted Answer

(i) 70.5°; (ii) N = (-2,-1,2); (iii) (-9, 6, -3/2); (iv) r = (-4,-2,4) + μ(10,-16,11)

NJC Vectors II Tutorial Q5

NJC Vectors II Tutorial Q5

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