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: 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})