The position vectors of the points $A$, $B$ and $C$, relative to the origin $O$ are \(\mathb

Question

The position vectors of the points $A$, $B$ and $C$, relative to the origin $O$ are $\mathbf{a}=\,\mathbf{i}+2\mathbf{k}$, $\mathbf{b}=3\mathbf{i}+\mathbf{j}+3\mathbf{k}$ and $\mathbf{c}=\,\mathbf{i}+\mathbf{j}+\mathbf{k}$ respectively. Determine whether the points $A$, $B$ and $C$ are collinear.[2] The point $D$ on the line segment $AB$ is such that $AD:DB=k:1-k$. Find the value of $k$ such that $CD$ bisects the angle $ACB$.[4]

Accepted Answer

(i) $A,B,C$ are not collinear. (ii) $k=\dfrac13$

2013 TJC P2 Q2

2013 TJC P2 Q2

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