جواب کار در کلاس صفحه 73 درس 3 هندسه دوازدهم (بردارها)

الف

\(\overrightarrow a + \overrightarrow b = (3/5\;,\;2) + ( - 1\;,\;2) = (2/5\;,\;4)\)

ب

\(\begin{array}{l}\overrightarrow c = ( - 2\;,\; - 3) \Rightarrow - \overrightarrow c = (2\;,\;3)\\\\\overrightarrow b = ( - 1\;,\;2) \Rightarrow - \overrightarrow b = (1\;,\; - 2)\end{array}\)

ج

\(\begin{array}{l}\overrightarrow a - \overrightarrow b = \overrightarrow a + ( - \overrightarrow b ) = (3/5\;,\;2) + (1\;,\; - 2)\\ = (4/5\;,\;0) \Rightarrow \left| {\overrightarrow a - \overrightarrow b } \right| = 4/5\\\\\overrightarrow d - \overrightarrow c = \overrightarrow d + ( - \overrightarrow c ) = (2\;,\; - 3) + (2\;,\; - 3)\\ = (4\;,\;0) \Rightarrow \left| {\overrightarrow d - \overrightarrow c } \right| = 4\end{array}\)

د

\(\begin{array}{l}\overrightarrow a = (3/5\;,\;2) \Rightarrow \overrightarrow a = 3/5\,\overrightarrow i + 2\,\overrightarrow j \\\\\overrightarrow b = ( - 1\;,\;2) \Rightarrow \overrightarrow b = - \,\overrightarrow i + 2\,\overrightarrow j \\\\\overrightarrow c = ( - 2\;,\; - 3) \Rightarrow \overrightarrow c = - 2\,\overrightarrow i - 3\,\overrightarrow j \\\\\overrightarrow d = (2\;,\; - 3) \Rightarrow \overrightarrow d = 2\,\overrightarrow i - 3\,\overrightarrow j \\\\\overrightarrow a + \overrightarrow b = (2/5\;,\;4) \Rightarrow \overrightarrow a + \overrightarrow b = 2/5\,\overrightarrow i + 4\,\overrightarrow j \\\\\overrightarrow a - \overrightarrow b = (4/5\;,\;0) \Rightarrow \overrightarrow a - \overrightarrow b = 4/5\,\overrightarrow i \\\\\overrightarrow d - \overrightarrow c = (4\;,\;0) \Rightarrow \overrightarrow d - \overrightarrow c = 4\,\overrightarrow i \end{array}\)