If \(\overrightarrow{OX} = \begin{pmatrix} -7 \\ 6 \end{pmatrix}\) and \(\overrightarrow{OY} = \begin{pmatrix} 16 \\ -11 \end{pmatrix}\), find \(\overrightarrow{YX}\).

A.

\(\begin{pmatrix} 9 \\ -5 \end{pmatrix}\)

B.

\(\begin{pmatrix} -23 \\ -5 \end{pmatrix}\)

C.

\(\begin{pmatrix} 9 \\ 17 \end{pmatrix}\)

D.

\(\begin{pmatrix} -23 \\ 17 \end{pmatrix}\)

Correct answer is D

\(\overrightarrow{OY} \equiv -\overrightarrow{YO}\)

Also, \(\overrightarrow{YO} + \overrightarrow{OX} = \overrightarrow{YX}\)

\(\therefore \overrightarrow{YO} = -\overrightarrow{OY} = - \begin{pmatrix} 16 \\  -11  \end{pmatrix} = \begin{pmatrix} -16 \\ 11  \end{pmatrix}\)

\(\overrightarrow{YX} = \begin{pmatrix}  -16 \\ 11  \end{pmatrix}  + \begin{pmatrix}  -7  \\  6   \end{pmatrix}\)

= \(\begin{pmatrix}  -23  \\  17  \end{pmatrix}\)