共50条信息
已知向量\(a=(-2,1)\),\(b=(-1,3)\),则
已知平面向量\(\overrightarrow{a}=(1,2) \overrightarrow{b}=(-3,2) \),若\(k \overrightarrow{a}+ \overrightarrow{b} \)与\(\overrightarrow{a}-3 \overrightarrow{b} \)垂直,则实数\(k\)值为
向量\(\overrightarrow{a}=(1,x+1),\overrightarrow{b}=(1-x,2),\overrightarrow{a}\bot \overrightarrow{b},\)则\(\left( \overrightarrow{a}+\overrightarrow{b} \right)\cdot \left( \overrightarrow{a}-\overrightarrow{b} \right)=\)______.
已知向量\(\overrightarrow{a}{=}(1{,}m){,}\overrightarrow{b}{=}(3{,-}2)\),且\((\overrightarrow{a}{+}\overrightarrow{b}){⊥}\overrightarrow{b}\),则\(m{=}({ })\)
从集合\(\{2,3,4,5\}\)中随机抽取一个数\(a\),从集合\(\{1,3,5\}\)中随机抽取一个数\(b\),则向量\(m=(a,b)\)与向量\(n=(1,-1)\)垂直的概率为________.
已知平面向量\(a=\left(1,2\right) \),\(b=\left(-3,2\right) \),若\(ka+b\)与\(a\)垂直,则实数\(k\)值为\((\) \()\)
已知向量\(a\),\(b\),其中\(a=(1,\sqrt{3})\),且\(a⊥(a-3b)\),则\(b\)在\(a\)上的投影为\((\) \()\)
已知平面向量\(\overrightarrow{a}\),\(\overrightarrow{b}\)是非零向量,\(|\overrightarrow{a}|=2\),\(\overrightarrow{a}\bot \left( \overrightarrow{a}+2\overrightarrow{b} \right)\),则向量\(\overrightarrow{b}\)在向量\(\overrightarrow{a}\)方向上的投影为\((\) \()\)
已知\(\overrightarrow{AB}\)与\(\overrightarrow{AC}\)的夹角为\(90^{\circ}\),\(\overrightarrow{|AB|}=2\),\(\overrightarrow{AC}=1\),\(\overrightarrow{AM}=\lambda \overrightarrow{AB}+\mu \overrightarrow{AC}(λ,μ∈R)\),且\(\overrightarrow{AM}\cdot \overrightarrow{BC}=0\),则\(\dfrac{\lambda }{\mu }\)的值为________.
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