جواب کاردرکلاس صفحه 108 درس 8 ریاضی هفتم (بردار و مختصات)

\(\begin{array}{l}\left[ \begin{array}{l} - 2\\\;1\end{array} \right] + \left[ \begin{array}{l}x\\y\end{array} \right] = \left[ \begin{array}{l}\;3\\ - 2\end{array} \right]\\\\ - 2 + x = 3\;\;,\;\;1 + y = - 2\\\\ \Rightarrow \left\{ \begin{array}{l}x = 5\\\\y = - 3\end{array} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,\left[ {\begin{array}{*{20}{c}}5\\{ - 3}\end{array}} \right]\\\\\left[ \begin{array}{l}x\\y\end{array} \right] + \left[ \begin{array}{l} - 1\\\;2\end{array} \right] = \left[ \begin{array}{l}\;2\\ - 1\end{array} \right]\\\\x - 1 = 2\;\;,\;\;y + 2 = - 1\\\\ \Rightarrow \left\{ \begin{array}{l}x = 3\\\\y = - 3\end{array} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,\left[ {\begin{array}{*{20}{c}}3\\{ - 3}\end{array}} \right]\\\\\left[ \begin{array}{l} - 4\\\;3\end{array} \right] + \left[ \begin{array}{l}\;2\\ - 1\end{array} \right] = \left[ \begin{array}{l}\;x\\ - y\end{array} \right]\\\\ - 4 + 2 = x\;\;,\;\;3 - 1 = - y\\\\ \Rightarrow \left\{ \begin{array}{l}x = - 2\\\\y = - 2\end{array} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{ - 2}\\{ - 2}\end{array}} \right]\end{array}\)

مختصات ابتدا – مختصات انتها = مختصات بردار

\( = \left[ \begin{array}{l}3\\0\end{array} \right] - \left[ \begin{array}{l} - 1\\4\end{array} \right] = \left[ \begin{array}{l}3 - ( - 1)\\0 - 4\end{array} \right] = \left[ \begin{array}{l}4\\ - 4\end{array} \right]\) مختصات بردار