优优班--学霸训练营 > 知识点挑题
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            • 1.

              已知向量\(\overrightarrow{a}=(1,2)\),\(\overrightarrow{b}=(3,-4)\),则\(\overrightarrow{a}\)在\(\overrightarrow{b}\)上的投影为\((\)   \()\)

              A.\(-1\)          
              B.\(-\sqrt{5}\)
              C.\(1\)
              D.\(\sqrt{5}\) 
            • 2.

              在\(∆ABC \)中,\(\left| \overrightarrow{AB}+ \overrightarrow{AC}\right|=\left| \overrightarrow{AB}- \overrightarrow{AC}\right| \),\(AB=4\),\(AC=3\),则\(\overrightarrow{BC} \)在\(\overrightarrow{CA} \)方向上的投影是\((\)   \()\)

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

              在\(\triangle ABC\)中,\(AB=3,AC=2,\angle BAC={{60}^{0}}\),\(M\)是\(BC\)的中点,\(N\)在直线\(AM\)上,且\(BN\bot AM\),则向量\(\overrightarrow{BN}\)在向量\(\overrightarrow{AC}\)上的投影为\((\)    \()\)

              A.\(-\dfrac{27}{19}\)
              B.\(-\dfrac{27}{38}\)
              C.\(\dfrac{27}{19}\)
              D.\(\dfrac{27}{38}\)
            • 4.

              \(4.\)在边长为\(2\)的菱形\(ABCD\)中,\(∠BAD={120}^{0} \),则\(\overrightarrow{AC} \)在\(\overrightarrow{AB} \)方向上的投影为\((\)   \()\)

              A.\(\dfrac{1}{4} \)
              B.\(\dfrac{1}{2} \)
              C.\(1\)
              D.\(2\)
            • 5.

              已知向量\( \overset{→}{a}, \overset{→}{b} \)的夹角\(\left| \overset{→}{a}\right|=1 \)为\(120^{\circ} \),且,\(\left| \overset{→}{b}\right|=2 \),则向量\( \overset{→}{a}+ \overset{→}{b} \)在向量\( \overset{→}{a} \)方向上的投影是

              A.\(0\)
              B.\( \dfrac{2}{3} \)
              C.\(-1\)
              D.\( \dfrac{1}{2} \)
            • 6. \((B\)类题\()\)若点\(P\)是\(\triangle ABC\)的外心,且\( \overset{→}{PA}+ \overset{→}{PB}+λ \overset{→}{PC}=0 \),\(∠C=120^{\circ}\),则实数\(λ\)的值为\((\) \()\)
              A.\( \dfrac{1}{2} \)
              B.\(− \dfrac{1}{2} \)
              C.\(-1\)
              D.\(1\)
            • 7.

              向量\( \overset{→}{a}, \overset{→}{b} \)的夹角为\(120^{\circ} \),且\(\left| \overset{→}{a}\right|=1 \),\(\left| \overset{→}{b}\right|=2 \),则向量\( \overset{→}{a}+ \overset{→}{b} \)在向量\( \overset{→}{a} \)方向上的投影是\((\)   \()\)

              A.\(0\)
              B.\( \dfrac{2}{3} \)
              C.\(-1\)
              D.\( \dfrac{1}{2} \)
            • 8. 已知\(| \overrightarrow{a}|=5,| \overrightarrow{b}|=4, \overrightarrow{a}\)与\( \overrightarrow{b}\)夹角\(θ=120^{\circ}\),则向量\( \overrightarrow{b}\)在向量\( \overrightarrow{a}\)上的投影为\((\)  \()\)
              A.\(-2\)
              B.\(2\)
              C.\( \dfrac {5}{2}\)
              D.\(- \dfrac {5}{2}\)
            • 9. 已知\(| \overrightarrow{a}|=5 \),\(| \overrightarrow{b}|=3 \),且\( \overrightarrow{a}⋅ \overrightarrow{b}=-12 \),则向量\( \overrightarrow{a}\)在向量\( \overrightarrow{b}\)上的投影等于\((\)  \()\)
              A.\( \dfrac {12}{5}\)
              B.\(4\)
              C.\(- \dfrac {12}{5}\)
              D.\(-4\)
            • 10.
              如图,点\(P\)是圆\(C\):\(x^{2}+(y-2 \sqrt {2})^{2}=1\)上的一个动点,点\(Q\)是直线\(l\):\(x-y=0\)上的一个动点,\(O\)为坐标原点,则向量\( \overrightarrow{OP}\)在向量\( \overrightarrow{OQ}\)上的射影的数量的最大值是\((\)  \()\)
              A.\(3\)
              B.\(2+ \dfrac { \sqrt {2}}{2}\)
              C.\(3 \sqrt {2}\)
              D.\(1\)
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