If \(\overrightarrow{OX} = \begin{pmatrix} -7 \\ 6 \end{pmatrix}\) and \(\overrightarrow{OY} = \begin{pmatrix} 16 \\ -11 \end{pmatrix}\), find \(\overrightarrow{YX}\).
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Correct Answer: Option D
Explanation:
\(\overrightarrow{OY} \equiv -\overrightarrow{YO}\)
Also, \(\overrightarrow{YO} + \overrightarrow{OX} = \overrightarrow{YX}\)
\(\therefore \overrightarrow{YO} = -\overrightarrow{OY} = - \begin{pmatrix} 16 \\ -11 \end{pmatrix} = \begin{pmatrix} -16 \\ 11 \end{pmatrix}\)
\(\overrightarrow{YX} = \begin{pmatrix} -16 \\ 11 \end{pmatrix} + \begin{pmatrix} -7 \\ 6 \end{pmatrix}\)
= \(\begin{pmatrix} -23 \\ 17 \end{pmatrix}\)
\(\overrightarrow{OY} \equiv -\overrightarrow{YO}\)
Also, \(\overrightarrow{YO} + \overrightarrow{OX} = \overrightarrow{YX}\)
\(\therefore \overrightarrow{YO} = -\overrightarrow{OY} = - \begin{pmatrix} 16 \\ -11 \end{pmatrix} = \begin{pmatrix} -16 \\ 11 \end{pmatrix}\)
\(\overrightarrow{YX} = \begin{pmatrix} -16 \\ 11 \end{pmatrix} + \begin{pmatrix} -7 \\ 6 \end{pmatrix}\)
= \(\begin{pmatrix} -23 \\ 17 \end{pmatrix}\)