优优班--学霸训练营 > 知识点挑题
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            • 1.
              若\( \overrightarrow{a}=(2x,1,3)\),\( \overrightarrow{b}=(1,-2y,9)\),如果\( \overrightarrow{a}\)与\( \overrightarrow{b}\)为共线向量,则\((\)  \()\)
              A.\(x=1\),\(y=1\)
              B.\(x= \dfrac {1}{2}\),\(y=- \dfrac {1}{2}\)
              C.\(x= \dfrac {1}{6}\),\(y=- \dfrac {3}{2}\)
              D.\(x=- \dfrac {1}{6}\),\(y= \dfrac {3}{2}\)
            • 2.
              已知向量\( \overrightarrow{a}=(2,4,5)\),\( \overrightarrow{b}=(3,x,y)\)分别是直线\(l_{1}\)、\(l_{2}\)的方向向量,若\(l_{1}/\!/l_{2}\),则\((\)  \()\)
              A.\(x=6\),\(y=15\)
              B.\(x=3\),\(y= \dfrac {15}{2}\)
              C.\(x=3\),\(y=15\)
              D.\(x=6\),\(y= \dfrac {15}{2}\)
            • 3.
              已知向量\( \overrightarrow{a}=(2,4,5)\),\( \overrightarrow{b}=(3,x,y)\),分别是直线\(l_{1}\)、\(l_{2}\) 的方向向量,若\(l_{1}/\!/l_{2}\),则\((\)  \()\)
              A.\(x=6\),\(y=15\)
              B.\(x=3\),\(y=15\)
              C.\(x= \dfrac {8}{3}\),\(y= \dfrac {10}{3}\)
              D.\(x=6\),\(y= \dfrac {15}{2}\)
            • 4.
              已知直线\(l\)的方向向量\( \overrightarrow{m}=(2,m,1)\),平面\(α\)的法向量\( \overrightarrow{n}=(1, \dfrac {1}{2},2)\),且\(l/\!/α\),则\(m=(\)  \()\)
              A.\(8\)
              B.\(-8\)
              C.\(1\)
              D.\(-1\)
            • 5.

              已知向量\(\overrightarrow{a}=(\lambda +1,0,2\lambda ),\overrightarrow{b}=(6,2\mu -1,2)\) ,若\(\overrightarrow{a}/\!/\overrightarrow{b}\),则\(\lambda \)与\(\mu \)的值分别为

              A.\(\dfrac{1}{5},\dfrac{1}{2}\)
              B.\(5,2\)
              C.\(-\dfrac{1}{5},-\dfrac{1}{2}\)
              D.\(-5,-2\)
            • 6.

              已知向量\(\overset{\to }{{a}}\,=(2,-1,3)\),\(\overset{\to }{{b}}\,=(-4,2,x)\),使\(\overset{\to }{{a}}\,/\!/\overset{\to }{{b}}\,\)成立的\(x\)为(    )

              A.\(-6\)
              B.\(6\)
              C.\(\dfrac{10}{3}\)
              D.\(-\dfrac{10}{3}\)
            • 7.

              \(=(2,3,\)\(m\)\()\),\(=(2\)\(n\),\(6\),\(8)\)且为共线向量,则\(m\)\(+\)\(n\)的值为(    )

              A.\(7\)      
              B.
              C.\(6\)
              D.\(8\)
            • 8.

              已知数列\(\left\{ {{a}_{n}} \right\}\)是等差数列,\(A\)、\(B\)、\(C\)、\(D\)四点共面\((\)任意三点不共线\()\),\(O\)是空间中任意一点,且满足\(\overrightarrow{OA}={{a}_{5}}\overrightarrow{OB}+{{a}_{7}}\overrightarrow{OC}+{{a}_{9}}\overrightarrow{OD}\),则数列\(\left\{ {{a}_{n}} \right\}\)的前\(13\)项和为\((\) \()\)

              A.\(13\)   
              B.\(\dfrac{13}{3}\)
              C.\(\dfrac{13}{2}\)
              D.\(\dfrac{13}{4}\)
            • 9.

              已知\(A\)、\(B\)、\(C\)是不共线的三点,\(O\)是平面\(ABC\)外一点,则在下列条件中,能得到点\(M\)与\(A\)、\(B\)、\(C\)一定共面的条件是(    )

              A.     
              B.  
              C.       
              D.
            • 10.
              设平面\(α\)的一个法向量为\( \overrightarrow{n_{1}}=(1,2,-2)\),平面\(β\)的一个法向量为\( \overrightarrow{n_{2}}=(-2,-4,k)\),若\(α/\!/β\),则\(k=(\)  \()\)
              A.\(2\)
              B.\(-4\)
              C.\(-2\)
              D.\(4\)
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