Câu hỏi
Cho \(\vec a = \left( {2;1} \right),\;\vec b = \left( {3;4} \right),\;\vec c = \left( {7;2} \right).\)
a) Tìm tọa độ của vecto \(\vec u = 2\vec a - 3\vec b + \vec c.\)
b) Tìm tọa độ của vecto \(\vec v\)ao cho \(\vec v + \vec a = \vec b - \vec c.\)
c) Tìm các số \(k,\,\,m\) để \(\vec c = k\vec a + m\vec b.\)
- A \(\begin{array}{l}
a)\,\,\overrightarrow u = \left( {2;\,\,8} \right)\\
b)\,\,\overrightarrow v = \left( { - 6;\,\,1} \right)\\
c)\,\,\overrightarrow c = \frac{{22}}{5}\overrightarrow a - \frac{3}{5}\overrightarrow b
\end{array}\) - B \(\begin{array}{l}
a)\,\,\overrightarrow u = \left( {2;\, - \,8} \right)\\
b)\,\,\overrightarrow v = \left( { - 6;\,\,1} \right)\\
c)\,\,\overrightarrow c = \frac{{22}}{5}\overrightarrow a - \frac{3}{5}\overrightarrow b
\end{array}\) - C \(\begin{array}{l}
a)\,\,\overrightarrow u = \left( {2;\, - \,8} \right)\\
b)\,\,\overrightarrow v = \left( {6;\,\,1} \right)\\
c)\,\,\overrightarrow c = \frac{{22}}{5}\overrightarrow a - \frac{3}{5}\overrightarrow b
\end{array}\) - D \(\begin{array}{l}
a)\,\,\overrightarrow u = \left( {2;\, - \,8} \right)\\
b)\,\,\overrightarrow v = \left( { - 6;\,\,1} \right)\\
c)\,\,\overrightarrow c = \frac{{22}}{5}\overrightarrow a + \frac{3}{5}\overrightarrow b
\end{array}\)
Lời giải chi tiết:
\(\begin{array}{l}a)\,\,\vec u = 2\vec a - 3\vec b + \vec c = \left( {4;\,2} \right) - \left( {9;12} \right) + \left( {7;2} \right) = \left( {2; - 8} \right)\\b)\,\,\overrightarrow v + \overrightarrow a = \overrightarrow b - \overrightarrow c \Leftrightarrow \overrightarrow v = - \overrightarrow a + \overrightarrow b - \overrightarrow c \\ \Leftrightarrow \overrightarrow v = - \left( {2;\,\,1} \right) + \left( {3;\,\,4} \right) - \left( {7;\,\,2} \right)\\ \Leftrightarrow \overrightarrow v = \left( { - 2 + 3 - 7;\,\, - 1 + 4 - 2} \right) = \left( { - 6;\,\,1} \right)\\c)\,\,\overrightarrow c = k\overrightarrow a + m\overrightarrow b = k\left( {2;\,\,1} \right) + m\left( {3;\,\,4} \right)\\ \Leftrightarrow \left( {7;\,\,2} \right) = \left( {2k + 3m;\,\,k + 4m} \right)\\ \Leftrightarrow \left\{ \begin{array}{l}2k + 3m = 7\\k + 4m = 2\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}k = \frac{{22}}{5}\\m = - \frac{3}{5}\end{array} \right. \Rightarrow \overrightarrow c = \frac{{22}}{5}\overrightarrow a - \frac{3}{5}\overrightarrow b .\end{array}\)
Câu hỏi trước
