优优班--学霸训练营 > 知识点挑题
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            • 1.

              已知\({|}\overrightarrow{a}{|=}3{,}{|}\overrightarrow{b}{|=}5{,}\overrightarrow{a}{⋅}\overrightarrow{b}{=}12\),则向量\(\overrightarrow{a}\)在向量\(\overrightarrow{b}\)上的投影为\((\ \ \ \ \ \ \ \ \ {  })\)

              A.\(\dfrac{12}{5}\)
              B.\(3\)
              C.\(4\)
              D.\(5\)
            • 2.

              若\(\overrightarrow{a}{=}(2{,}3){,}\overrightarrow{b}{=}({-}4{,}7)\),则\(\overrightarrow{a}\)在\(\overrightarrow{b}\)方向上的投影为\(({  })\)

              A.\(\sqrt{3}\)
              B.\(\dfrac{\sqrt{13}}{5}\)
              C.\(\dfrac{\sqrt{65}}{5}\)
              D.\(\sqrt{65}\)
            • 3.
              已知\(| \overrightarrow{a}|=3\),\(| \overrightarrow{b}|=5\),\( \overrightarrow{a}\cdot \overrightarrow{b}=12\),则向量\( \overrightarrow{a}\)在向量\( \overrightarrow{b}\)上的投影为\((\)  \()\)
              A.\( \dfrac {12}{5}\)
              B.\(3\)
              C.\(4\)
              D.\(5\)
            • 4.

              已知向量\( \overset{→}{a} =(1, \sqrt{3} )\),\( \overset{→}{b} =(3,m)\),若向量\( \overset{→}{b} \)在\( \overset{→}{a} \)方向上的投影为\(3\),则实数\(m=\)(    )

              A.\(3\)     
              B.\(-3\)  
              C.\( \sqrt{3} \)
              D.\(-3 \sqrt{3} \)
            • 5.

              已知\(|\overrightarrow{a}|=2\),\(2\overrightarrow{a}-\overrightarrow{b}\bot \overrightarrow{a}\),则\(\overrightarrow{b}\)在\(\overrightarrow{a}\)方向上的投影为\((\)  \()\)

              A.\(-4\)
              B.\(-2\)
              C.\(2\)
              D.\(4\)
            • 6.

              如果\( \overset{→}{a}· \overset{→}{b}= \overset{→}{a}· \overset{→}{c} \)且\( \overset{→}{a} \neq 0\),那么\((\)    \()\)

              A.\(\overrightarrow{b}=\overrightarrow{c}\)
              B.\(\overrightarrow{b}=\lambda \overrightarrow{c}\)
              C.\(\overrightarrow{b}\bot \overrightarrow{c}\)
              D.\(\overrightarrow{b},\overrightarrow{c}\)在\(\overrightarrow{a}\)上的投影相等
            • 7.

              已知\(| \overrightarrow{a}|=6,| \overrightarrow{b}|=3, \overrightarrow{a}· \overrightarrow{b}=-12 \),则向量\(\overset{\to }{{a}}\,\)在向量\(\overset{\to }{{b}}\,\)方向上的投影为(    )

              A.\(-4\)      
              B.\(4\)           
              C.\(-2\)          
              D.\(2\)
            • 8.

              已知\(\left| \overset{⇀}{a}\right|=2 \), \(\left| \overset{⇀}{b}\right|=1 \),\(\overrightarrow{a}\cdot \overrightarrow{b}=1\),则向量\(\overrightarrow{a}\)在\(\overrightarrow{b}\)方向上的投影是

              A.\(-\dfrac{1}{2}\)
              B.\(-1\)
              C.\(\dfrac{1}{2}\)
              D.\(1\)
            • 9. 已知|
              a
              |=5,|
              b
              |=3,且
              a
              b
              =-12,则向量
              a
              在向量
              b
              上的投影等于(  )
              A.
              12
              5
              B.4
              C.-
              12
              5
              D.-4
            • 10. 已知
              a
              b
              =12,且|
              a
              |=3,|
              b
              |=5
              b
              a
              方向上的投影为(  )
              A.
              4
              5
              B.
              12
              5
              C.4
              D.-4
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