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) $\overrightarrow{AB}=\left( \begin{matrix} -4 \ 2 \ \end{matrix} \right)$, $\overrightarrow{PB}=\left( \begin{matrix} -6 \ -4 \ \end{matrix} \right)$ (ii) $\left( \begin{matrix} 2 \ 6 \ \end{matrix} \right)$ (iii) $\left( \begin{matrix} 10 \ 2 \ \end{matrix} \right)$

Vectors - Vectors in a Parallelogram

Vectors - Vectors in a Parallelogram