<ol class="abc-list"><li><ol class="i-list"><li><div class="list-item-paragraph">Find the shortest distance from the origin $O$ to the plane $p$ with equation $2x+3y+6z=10$.<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Given that point $A$ lies on plane $p$ and $OA=10$, find the acute angle between the plane $p$ and $OA$.<span class="inline-marks">[2]</span></div></li></ol></li><li><div class="list-item-paragraph">Two non-zero vectors $\mathbf{a}$ and $\mathbf{b}$ are such that&nbsp;$\left| \mathbf{a}\times \mathbf{b} \right|=\sqrt{3}$, $\left| \mathbf{a}-\mathbf{b} \right|=1$ and the angle between the vectors $\mathbf{a}$ and $\mathbf{b}$ is ${{30}^{\circ }}$, find the possible values of $\left| \mathbf{a} \right|$ and $\left| \mathbf{b} \right|$.<span class="inline-marks">[5]</span></div></li><li><div class="list-item-paragraph">Two fixed points $C$ and $D$ have position vectors $\mathbf{c}$ and $\mathbf{d}$ respectively. By considering the result $\mathbf{c}\times \mathbf{c}=\mathbf{0}$, give a geometrical interpretation of the vector equation $\mathbf{r}\times \left( \mathbf{d}-\mathbf{c} \right)=\mathbf{c}\times \mathbf{d}$.<span class="inline-marks">[3]</span></div></li></ol>

Two non-zero vectors $\mathbf{a}$ and $\mathbf{b}$ are such that $\left| \mathbf{a}\times \mathbf{b} \right|=\sqrt{3}$, $\left| \mathbf{a}-\mathbf{b} \right|=1$ and the angle between the vectors $\mathbf{a}$ and $\mathbf{b}$ is ${{30}^{\circ }}$, find the possible values of $\left| \mathbf{a} \right|$ and $\left| \mathbf{b} \right|$.

Two fixed points $C$ and $D$ have position vectors $\mathbf{c}$ and $\mathbf{d}$ respectively. By considering the result $\mathbf{c}\times \mathbf{c}=\mathbf{0}$, give a geometrical interpretation of the vector equation $\mathbf{r}\times \left( \mathbf{d}-\mathbf{c} \right)=\mathbf{c}\times \mathbf{d}$.

2023 NJC Promo Q5

2023 NJC Promo Q5

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