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Vectors - Vectors in a Parallelogram

Vectors - Vectors in a Parallelogram

Secondary 4

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

Points A, B, and P on a coordinate grid
  1. Express \(\overrightarrow{AB}\) and \(\overrightarrow{PB}\) as column vectors.
  2. \(Q\) is a point such that \(ABQP\) is a parallelogram. Express \(\overrightarrow{BQ}\) as a column vector.
  3. \(R\) is a point such that \(ABPR\) is a parallelogram. Express \(\overrightarrow{BR}\) as a column vector.
  4. Do the two vectors \(\overrightarrow{PQ}\) and \(\overrightarrow{PR}\) have the same magnitude? Is \(\overrightarrow{PQ} = \overrightarrow{PR}\)? Explain.

Solution:

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Answer:(i) \(\overrightarrow{AB}=\begin{pmatrix}-4\\ 2\end{pmatrix},\;\overrightarrow{PB}=\begin{pmatrix}-6\\ -4\end{pmatrix}\) (ii) \(\overrightarrow{BQ}=\begin{pmatrix}2\\ 6\end{pmatrix}\) (iii) \(\overrightarrow{BR}=\begin{pmatrix}10\\ 2\end{pmatrix}\) (iv) Both magnitudes are \(2\sqrt5\) units; the vectors are unequal because they have opposite directions.

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