The line $l$ passes through the points$A$ and $B$ with coordinates $\left( 1,2,4 \right)$ and $\left

Question

The line $l$ passes through the points$A$ and $B$ with coordinates $\left( 1,2,4 ight)$ and $\left( -5,4,-2 ight)$ respectively. The plane $p$ has equation $\mathbf{r}=\left(\begin{matrix}0 \-17\0 \\end{matrix} ight)+\lambda\left( \begin{matrix}1 \17 \7 \\end{matrix} ight)+\mu\left( \begin{matrix}1 \3 \0 \ \end{matrix} ight)$, where $\lambda ,\mu \in \mathbb{R}$. Show that the plane $p$ has Cartesian equation $3x-y+2z=17$. [3] Find the coordinates of the point of intersection of $l$ and $p$. [4] Find the acute angle between $l$ and $p$. [2] Find the exact perpendicular distance from $B$ to $p$ . [2]

Accepted Answer

(i) $3x-y+2z=17$ (ii) $\displaystyle \left(\frac{5}{2},\frac{3}{2},\frac{11}{2}\right)$ (iii) $78.8^{\circ}$ (iv) $\displaystyle \frac{40}{\sqrt{14}}=\frac{20\sqrt{14}}{7}$ units

2011 IJC P1 Q10

2011 IJC P1 Q10

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