The $1$ unit by $1$ unit square grid below shows the positions of point $A$, $B$ and $P$.

Question

The $1$ unit by $1$ unit square grid below shows the positions of point $A$, $B$ and $P$. Express $\overrightarrow{AB}$ and $\overrightarrow{PB}$ as column vectors. $Q$ is a point such that $ABQP$ is a parallelogram. Express $\overrightarrow{BQ}$ as a column vector. $R$ is a point such that $ABPR$ is a parallelogram. Express $\overrightarrow{BR}$ as a column vector. Do the two vectors $\overrightarrow{PQ}$ and $\overrightarrow{PR}$ have the same magnitude? Is $\overrightarrow{PQ} = \overrightarrow{PR}$? Explain.

Accepted Answer

(i) $\overrightarrow{AB}=\begin{pmatrix}-5\-3\end{pmatrix}$, $\overrightarrow{PB}=\begin{pmatrix}1\-5\end{pmatrix}$ (ii) $\overrightarrow{BQ}=\begin{pmatrix}-6\2\end{pmatrix}$ (iii) $\overrightarrow{BR}=\begin{pmatrix}4\8\end{pmatrix}$ (iv) Same magnitude $\sqrt{34}$, but $\overrightarrow{PR}=-\overrightarrow{PQ}$

Vector Geometry within a Cartesian Plane

Vector Geometry within a Cartesian Plane

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