Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\overrightarrow{u}+2\overrightarrow{v}-3\overrightarrow{w}+\overrightarrow{x}=\overrightarrow{0}\)
\(\Rightarrow\overrightarrow{x}=3\overrightarrow{w}-\overrightarrow{u}-2\overrightarrow{v}=3\left(-5;7\right)-\left(2;-5\right)-2\left(3;4\right)=\left(-23;18\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a.
\(\overrightarrow{u}=2\left(2;1\right)-\left(3;4\right)=\left(1;-2\right)\)
\(\overrightarrow{v}=3\left(3;4\right)-2\left(7;2\right)=\left(-5;8\right)\)
\(\overrightarrow{w}=5\left(7;2\right)+\left(2;1\right)=\left(37;11\right)\)
b.
\(\overrightarrow{x}=2\left(2;1\right)+\left(3;4\right)-\left(7;2\right)=\left(0;4\right)\)
\(\overrightarrow{z}=2\left(2;1\right)-3\left(3;4\right)+\left(7;2\right)=\left(2;-8\right)\)
c.
\(\overrightarrow{w}+\overrightarrow{a}=\overrightarrow{b}-\overrightarrow{c}\Rightarrow\overrightarrow{w}=\overrightarrow{b}-\overrightarrow{c}-\overrightarrow{a}\)
\(\Rightarrow\overrightarrow{w}=\left(3;4\right)-\left(7;2\right)-\left(2;1\right)=\left(-6;1\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left|\overrightarrow{a}\right|=\sqrt{2^2+\left(-1\right)^2}=\sqrt{5}\)
\(\left|\overrightarrow{b}\right|=\sqrt{x^2+1}\)
\(\Rightarrow\sqrt{x^2+1}=\sqrt{5}\Rightarrow x^2=4\)
\(\Rightarrow x=2;x=-2\)
Độ dài vectơ a là:
√[2² + (-1)²] = √5
Để độ dài của vectơ a bằng độ dài của vectơ b thì:
x² + 1 = 5
x² = 4
x = -2; x = 2
Chọn C
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left\{{}\begin{matrix}\overrightarrow{AB}=\left(1;-1\right)\\\overrightarrow{BC}=\left(-3;4\right)\end{matrix}\right.\)
\(\Rightarrow\overrightarrow{u}=3\overrightarrow{AB}+2\overrightarrow{BC}=\left(-3;5\right)\)
Gọi \(D\left(x;y\right)\Rightarrow\overrightarrow{DC}=\left(1-x;5-y\right)\)
Để ABCD là hbh \(\Leftrightarrow\overrightarrow{AB}=\overrightarrow{DC}\)
\(\Leftrightarrow\left\{{}\begin{matrix}1-x=1\\5-y=-1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=0\\y=6\end{matrix}\right.\)
\(\Rightarrow D\left(0;6\right)\)
Lời giải:
\(\overrightarrow{a}-\overrightarrow{u}+2\overrightarrow{v}=\overrightarrow{0}\)
\(\Leftrightarrow (3-x;2)-(1;-2)+2(3;-1)=(0;0)\)
\(\Rightarrow \left\{\begin{matrix} 3-x-1+2.3=0\\ 2-(-2)+2(-1)=0\end{matrix}\right.\) (vô lý)
Em xin cảm ơn ạ