共50条信息
已知\(\vec{a}=(3,-2,1)\),\(\overrightarrow{b}=(-2,4,0)\),\(\overrightarrow{c}=(3,0,2)\),则\(\overrightarrow{a}-2\overrightarrow{b}+4\overrightarrow{c}=\)_______.
点\(P\)是棱长为\(1\)的正方体\(ABCD-A\)\(1\)\(B\)\(1\)\(C\)\(1\)\(D\)\(1\)的底面\(A\)\(1\)\(B\)\(1\)\(C\)\(1\)\(D\)\(1\)上一点,则\(\overrightarrow{PA}· \overrightarrow{P{C}_{1}} \)的取值范围是__________
如图所示,在正方体\(ABCD-{{A}_{1}}{{B}_{1}}{{C}_{1}}{{D}_{1}}\)中,以\(D\)为原点建立空间直角坐标系,\(E\)为\(B{{B}_{1}}\)的中点,\(F\)为\({{A}_{1}}{{D}_{1}}\)的中点,则下列向量能作为平面\(AEF\)的一个法向量的是( )
向量\(a\)\(=(-2,-3,1)\),\(b\)\(=(2,0,4)\),\(c\)\(=(-4,-6,2)\),下列结论正确的是\((\) \()\)
设向量\(a=(3,5,-4)\),\(b=(2,1,8)\).
\((1)\)计算\(2a+3b\),\(3a-2b\),\(a·b;\)
\((2)\)当\(λa+μb\)与\(z\)轴垂直时,求\(λ\),\(μ\)的关系式.
空间四边形\(ANCD\)中,若向量\( \overrightarrow{AB}=(-3,5,2) \),\( \overrightarrow{CD}=(-7,-1,-4) \),点\(E\),\(F\)分别为线段\(BC\),\(AD\)的中点,则\( \overrightarrow{EF} \)的坐标为( )
若\(\overrightarrow{a}{=}\left( 2{,}{-}1{,}0 \right)\),\(\overrightarrow{b}{=}(3{,}{-}4{,}7)\),且\((\lambda \overrightarrow{a}+\overrightarrow{b})⊥\overrightarrow{a}\)则\(\lambda\lambda \)的值是\((\) \()\)
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