优优班--学霸训练营 > 知识点挑题
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            • 1. 如图,四面体\(ABCD\)中,点\(E\)是\(CD\)的中点,记\( \overrightarrow{AB}= \overrightarrow{a}\),\( \overrightarrow{AC}= \overrightarrow{b}\),\( \overrightarrow{AD}= \overrightarrow{c}\),则\( \overrightarrow{BE}=(\)  \()\)
              A.\( \overrightarrow{a}- \dfrac {1}{2} \overrightarrow{b}+ \dfrac {1}{2} \overrightarrow{c}\)
              B.\(- \overrightarrow{a}+ \dfrac {1}{2} \overrightarrow{b}+ \dfrac {1}{2} \overrightarrow{c}\)
              C.\( \dfrac {1}{2} \overrightarrow{a}- \overrightarrow{b}+ \dfrac {1}{2} \overrightarrow{c}\)
              D.\(- \dfrac {1}{2} \overrightarrow{a}+ \overrightarrow{b}+ \dfrac {1}{2} \overrightarrow{c}\)
            • 2.

              \(①\)如果\(\overrightarrow{OP}= \dfrac{1}{2}\overrightarrow{OA}-\overrightarrow{OB}+ \dfrac{3}{2}\overrightarrow{OC}.\) 则\(P\),\(A\),\(B\),\(C\)四点共面\(;\)

              \(②\)若向量\(e_{1}\),\(e_{2}\),\(e_{3}\)是三个不共面的向量,且满足等式\(k_{1}e_{1}+k_{2}e_{2}+k_{3}e_{3}=0\),则\(k_{1}=k_{2}=k_{3}=0\).

              \(③\)已知空间向量\(a\),\(b\),\(c\),则对于空间的任意一个向量\(p\)总存在实数\(x\),\(y\),\(z\)使得\(p=xa+yb+zc\).

              \(④\)若\(p=xa+yb\),则\(p\)与\(a\),\(b\)共面;

              其中是真命题的序号是________\((\)把所有真命题的序号都填上\()\).

            • 3.

              点\(P(1,2,3)\)关于坐标平面\(xoy\)对称的点的坐标是\((\)  \()\) 

              A.\((-1,-2,3)\)   
              B.\((-1,2,3)\)    
              C.\((1,-2,3)\)      
              D.\((1,2,-3)\)
            • 4.

              在四面体\(ABCD\)中,\(E\),\(G\)分别是\(CD\),\(BE\)的中点,若空间向量\( \overset{→}{AG}=x \overset{→}{AB}+y \overset{→}{AD}+z \overset{→}{AC} \),则\(x+y+z=\)(    )

              A.\( \dfrac{1}{3} \)
              B.\( \dfrac{1}{2} \)
              C.\(1\)
              D.\(2\)
            • 5. 已知向量 \(a\)\(=(0,2,1)\), \(b\)\(=(-1,1,-2)\),则 \(a\)\(b\)的夹角为\((\)    \()\)
              A.\(0^{\circ}\)
              B.\(45^{\circ}\)
              C.\(90^{\circ}\)
              D.\(180^{\circ}\)
            • 6.

              如图,在四面体\(ABCD\)中,已知\(\overrightarrow{AB}=b\),\(\overrightarrow{AD}=a\),\(\overrightarrow{AC}\)\(=\)\(c\)\(\overrightarrow{BE}=\dfrac{1}{2}\overline{EC}\),则\(\overrightarrow{DE}\)等于                 \((\)  \()\).




              A.\(-a+\dfrac{2}{3}b+\dfrac{1}{3}c\)
              B.\(a+\dfrac{2}{3}b+\dfrac{1}{3}c\)

              C.\(a-\dfrac{2}{3}b+\dfrac{1}{3}c\)
              D.\(\dfrac{2}{3}a-b+\dfrac{1}{3}c\)
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