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            • 1.

              如图,以长方体\(ABCD-{{A}_{1}}{{B}_{1}}{{C}_{1}}{{D}_{1}}\)的顶点\(D\)为坐标原点,过点\(D\)的三条棱所在直线为坐标轴建立空间直角坐标系\(.\) 若\(\overrightarrow{D{{B}_{1}}}\)的坐标为\(\left(3,4,5\right) \),则\(\overrightarrow{{{A}_{1}}C}\)的坐标是




              A.\(\left(-3,4,-5\right) \)
              B.\(\left(-3,5,4\right) \)  

              C.\(\left(-3,4,5\right) \)
              D.\(\left(3,-4,5\right) \) 
            • 2. 如图所示,在空间直角坐标系中\(BC=2\),原点\(O\)是\(BC\)的中点,点\(A\)的坐标是\(( \dfrac { \sqrt {3}}{2}, \dfrac {1}{2},0)\),点\(D\)在平面\(yOz\)上,且\(∠BDC=90^{\circ}\),\(∠DCB=30^{\circ}\),则向量\( \overrightarrow{AD}\)的坐标为\((\)  \()\)
              A.\((- \dfrac { \sqrt {3}}{2},- \dfrac {1}{2}, \dfrac { \sqrt {3}}{2})\)
              B.\((- \dfrac { \sqrt {3}}{2},-1, \dfrac { \sqrt {3}}{2})\)
              C.\((- \dfrac {1}{2},- \dfrac { \sqrt {3}}{2}, \dfrac { \sqrt {3}}{2})\)
              D.\(( \dfrac { \sqrt {3}}{2},1, \dfrac { \sqrt {3}}{2})\)
            • 3.

              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(    ) 

                

              A.\((2,3,3)\)       
              B.\((-2,-3,-3)\)
              C.\((5,-2,1)\)     
              D.\((-5,2,-1)\)
            • 4.

              \((1)\)如图所示的水平放置的平面图形的直观图,它所表示的平面图形\(ABCD\)是 ______

              \((2)\) 若直线\(a/\!/α\),直线\(b\subset α\),则直线\(a\)与直线\(b\)的位置关系为 ______ .

              \((3)\)如图,在圆柱\(O_{1}O_{2}\)内有一个球\(O\),该球与圆柱的上、下底面及母线均相切,记圆柱\(O_{1}O_{2}\)的体积为\(V_{1}\),球\(O\)的体积为\(V_{2}\),则\(\dfrac{{{V}_{1}}}{{{V}_{2}}}\)的值是 ______


              \((4)\)如图,在棱长为\(1\)的正方体\(ABCD-A_{1}B_{1}C_{1}D_{1}\)中,点\(E\),\(F\)分别是棱\(BC\),\(CC_{1}\)的中点,\(P\)是侧面\(BCC_{1}B_{1}\)内一点,若\(A_{1}P/\!/\)平面\(AEF\),则线段\(A_{1}P\)长度的取值范围是 ______ .

            • 5. 三棱柱\(ABC-A_{1}B_{1}C_{1}\)中,若\( \overrightarrow{CA}= \overrightarrow{a}\),\( \overrightarrow{CB}= \overrightarrow{b}\),\( \overrightarrow{CC_{1}}= \overrightarrow{c}\),则\( \overrightarrow{A_{1}B}\)可用\( \overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}\)表示为\( \overrightarrow{A_{1}B}=\)______.
            • 6. 空间中,与向量\( \overrightarrow{a}=(3,0,4)\)同向共线的单位向量\( \overrightarrow{e}\)为\((\)  \()\)
              A.\( \overrightarrow{e}=(1,0,1)\)
              B.\( \overrightarrow{e}=(1,0,1)\)或\( \overrightarrow{e}=(-1,0,-1)\)
              C.\( \overrightarrow{e}=( \dfrac {3}{5},0, \dfrac {4}{5})\)
              D.\( \overrightarrow{e}=( \dfrac {3}{5},0, \dfrac {4}{5})\)或\( \overrightarrow{e}=(- \dfrac {3}{5},0,- \dfrac {4}{5})\)
            • 7. (2015秋•福建校级期末)如图,空间四边形OABC中,点M在OA上,且OM=2MA,点N为BC中点,
              MN
              =x
              OA
              +y
              OB
              +z
              OC
              ,则x,y,z的值分别是(  )
              A.-
              2
              3
              1
              2
              1
              2
              B.
              1
              2
              ,-
              2
              3
              1
              2
              C.
              1
              2
              1
              2
              ,-
              1
              2
              D.
              2
              3
              2
              3
              ,-
              1
              2
            • 8. 在四面体ABCD中,E、G分别是CD、BE的中点,若
              AG
              =x
              AB
              +y
              AD
              +z
              AC
              ,则x+y+z=(  )
              A.
              1
              3
              B.
              1
              2
              C.1
              D.2
            • 9. 已知空间任意一点O和不共线的三点A,B,C,若
              CP
              =2
              CA
              +
              CB
              ,则下列结论正确的是(  )
              A.
              OP
              =
              OA
              +2
              OB
              -2
              OC
              B.
              OP
              =-2
              OA
              -
              OB
              +3
              OC
              C.
              OP
              =2
              OA
              +
              OB
              -3
              OC
              D.
              OP
              =2
              OA
              +
              OB
              -2
              OC
            • 10. 已知A、B、C三点不共线,若点M与A、B、C四点共面,对平面ABC外一点O,给出下列表达式:
              OM
              =x
              OA
              +y
              OB
              +
              1
              3
              OC
              ,其中x,y是实数,则x+y=    
            0/40

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