A line $l$ passes through the points $A$ and $B$ with coordinates $(0, -2, 2)$ and \((1, 0,

Question

A line $l$ passes through the points $A$ and $B$ with coordinates $(0, -2, 2)$ and $(1, 0, 1)$ respectively. Find the acute angle between $\overrightarrow{OA}$ and the line $l$, where $O$ is the origin.[2] Hence, find the shortest distance from $O$ to the line $l$, leaving your answer in exact form.[1] A plane $\pi_1$ has equation $\mathbf{r} \cdot (2\mathbf{i} - \mathbf{j}) = 2$. Show that the line $l$ lies in the plane $\pi_1$.[2] A second plane $\pi_2$ contains the line $l$ and is perpendicular to the plane $\pi_1$. Find the cartesian equation of the plane $\pi_2$.[2]

Accepted Answer

(i) $30^\circ$ (ii) $\sqrt2$ units (iii) $l$ lies in $\pi_1$ (iv) $x+2y+5z=6$

2015 MI P1 Q7

2015 MI P1 Q7

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