<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1764587665402-g15x5vwqhvt.png" style="max-width: min(200px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>The figure shows a right pyramid $VABCD$ with a square base $ABCD$, standing horizontally on a cuboid $ABCDEFGH$. It is given that&nbsp;$VA=VB=VC=VD=5$ cm, $EF=FG=4$ cm and $AE=2$ cm, as shown in the diagram. $O$ is the centre of the square base $EFGH$. Perpendicular unit vectors $\mathbf{i},\mathbf{j},\mathbf{k}$ are parallel to $EF, FG, EA$ respectively.$C$ lies on $OA$ produced with $OC:AC=3:1$ and $D$ divides $OB$ in a ratio of $2:3$. $X$ is the point of intersection of $AB$ and $CD$.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Show that the height of the figure, $OV$ is $2+\sqrt{17}$.<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">State the geometrical meaning of $\frac{\left| \overrightarrow{VA}\times \overrightarrow{OV} \right|}{2+\sqrt{17}}$.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Find the equation of the line passing through $B$ and $V$.<span class="inline-marks">[2]</span></div></li></ol>

The figure shows a right pyramid $VABCD$ with a square base $ABCD$, standing horizontally on a cuboid $ABCDEFGH$. It is given that $VA=VB=VC=VD=5$ cm, $EF=FG=4$ cm and $AE=2$ cm, as shown in the diagram. $O$ is the centre of the square base $EFGH$. Perpendicular unit vectors $\mathbf{i},\mathbf{j},\mathbf{k}$ are parallel to $EF, FG, EA$ respectively.$C$ lies on $OA$ produced with $OC:AC=3:1$ and $D$ divides $OB$ in a ratio of $2:3$. $X$ is the point of intersection of $AB$ and $CD$.

Show that the height of the figure, $OV$ is $2+\sqrt{17}$.

State the geometrical meaning of $\frac{\left| \overrightarrow{VA}\times \overrightarrow{OV} \right|}{2+\sqrt{17}}$.

Find the equation of the line passing through $B$ and $V$.

Vectors - General

Vectors

H2 Math

International Baccalaureate Higher Level Mathematics

2013 SAJC P1 Q5

2013 SAJC P1 Q5

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