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Sums around a pentagon

Sums around a pentagon

Secondary 4
6 marks

\(JKLMN\) is a pentagon. Write each of the following as a single vector.

  1. \(\overrightarrow{JK}+\overrightarrow{KL}+\overrightarrow{LM}\)[1]
  2. \(\overrightarrow{NJ}+\overrightarrow{MN}\)[1]
  3. \(\overrightarrow{KL}+\overrightarrow{LM}+\overrightarrow{MN}+\overrightarrow{NK}\)[1]
  4. \(\overrightarrow{MN}+\overrightarrow{KL}+\overrightarrow{LM}\)[1]
  5. Given \(\mathbf{a}=\begin{pmatrix}3\\ -4\end{pmatrix}\) and \(\mathbf{b}=\begin{pmatrix}-1\\ 6\end{pmatrix}\), work out \(\mathbf{a}+\mathbf{b}\) and \(\mathbf{b}+\mathbf{a}\).[2]

Solution:

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Answer:(a) \(\overrightarrow{JM}\) (b) \(\overrightarrow{MJ}\) (c) \(\mathbf{0}\) (d) \(\overrightarrow{KN}\) (e) both \(\begin{pmatrix}2\\ 2\end{pmatrix}\)

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