The position vectors of points $A$, $B$ and $C$ with respect to the origin $O$ are $\mathbf{a}$, $\m

Question

The position vectors of points $A$, $B$ and $C$ with respect to the origin $O$ are $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$ respectively. It is given that $\overrightarrow{AC}=k\mathbf{a}-3\mathbf{b}$. State the value of $k$ such that $A$, $B$ and $C$ are collinear. Using the value of $k$ found in (i) and given that $\left| \mathbf{a} \right|=2$, $\mathbf{a}\cdot \mathbf{b}=3$, find the length of projection of $\overrightarrow{OC}$ on $\overrightarrow{OA}$.

Accepted Answer

(i) k = 3; (ii) 7/2 units

ASRJC Vectors Assignment Q1

ASRJC Vectors Assignment Q1

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