The line $l$ passes through the point $A$, whose position vector is $-\mathbf{i}+\mathbf{j}$,

Question

The line $l$ passes through the point $A$, whose position vector is $-\mathbf{i}+\mathbf{j}$, and is parallel to the vector $4\mathbf{i}-3\mathbf{j}+\mathbf{k}$ and the plane $p$ has equation $3x+\alpha y=26$. The plane $p$ is parallel to the line $l$. Show that $\alpha =4$.[2] Find the position vector of the foot of the perpendicular, $N$, from $A$ to the plane $p$.[4] Hence, find the coordinates of the point $B$ which is the mirror image of $A$ in $p$.[2] Find the area of triangle $OAB$, where $O$ is the origin.[2]

Accepted Answer

(i) $\alpha=4$. (ii) $\overrightarrow{ON}=(2,5,0)$. (iii) $B=(5,9,0)$. (iv) $7\text{ units}^2$.

2013 CJC P2 Q2

2013 CJC P2 Q2

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