<p>With respect to the origin, the points $A$, $B$ and $C$ have position vectors $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$ respectively with $\mathbf{a}$ not parallel to $\mathbf{b}$.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Show that $A$, $B$ and $C$ are collinear given that non-zero numbers $\lambda $ and $\mu $ are such that $\lambda \mathbf{a}+\mu \mathbf{b}+\mathbf{c}=0$; $\lambda +\mu +1=0$.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">Given that the point $P$ with position vector $\mathbf{p}$ lies on $BA$ produced such that $2\mathbf{p}=7\mathbf{a}-5\mathbf{b}$, find the ratio $AP:BP$.</div><p style="text-align: right;">[2]</p></li></ol>

With respect to the origin, the points $A$, $B$ and $C$ have position vectors $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$ respectively with $\mathbf{a}$ not parallel to $\mathbf{b}$.

Show that $A$, $B$ and $C$ are collinear given that non-zero numbers $\lambda $ and $\mu $ are such that $\lambda \mathbf{a}+\mu \mathbf{b}+\mathbf{c}=0$; $\lambda +\mu +1=0$.

Given that the point $P$ with position vector $\mathbf{p}$ lies on $BA$ produced such that $2\mathbf{p}=7\mathbf{a}-5\mathbf{b}$, find the ratio $AP:BP$.

Collinearity and Ratio Involving Position Vectors

Collinearity and Ratio Involving Position Vectors

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