优优班--学霸训练营 > 知识点挑题
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            • 1.
              已知向量\( \overrightarrow{a}\),\( \overrightarrow{b}\)满足\(| \overrightarrow{a}|=1\),且对任意实数\(x\),\(y\),\(| \overrightarrow{a}-x \overrightarrow{b}|\)的最小值为\( \dfrac { \sqrt {3}}{2}\),\(| \overrightarrow{b}-y \overrightarrow{a}|\)的最小值为\( \sqrt {3}\),则\(| \overrightarrow{a}+ \overrightarrow{b}|=(\)  \()\)
              A.\( \sqrt {7}\)
              B.\( \sqrt {5+2 \sqrt {3}}\)
              C.\( \sqrt {7}\)或\( \sqrt {3}\)
              D.\( \sqrt {5+2 \sqrt {3}}\)或\( \sqrt {5-2 \sqrt {3}}\)
            • 2.
              已知向量\( \overrightarrow{a}\),\( \overrightarrow{b}\)满足\(| \overrightarrow{a}|=1\),\(| \overrightarrow{b}|=2\),\( \overrightarrow{a}- \overrightarrow{b}=( \sqrt {3}, \sqrt {2})\),则\(|2 \overrightarrow{a}+ \overrightarrow{b}|=(\)  \()\)
              A.\(2 \sqrt {2}\)
              B.\( \sqrt {17}\)
              C.\( \sqrt {15}\)
              D.\(2 \sqrt {5}\)
            • 3.
              在直角坐标平面\(xOy\)上的一列点\(A_{1}(1,a_{1})\),\(A_{2}(2,a_{2})\),\(…\),\(A_{n}(2,a_{n})\),\(…\),简记为\(\{A_{n}\}\)若由\(b_{n}= \overrightarrow{A_{n}A_{n+1}}\cdot \overrightarrow{j}\)构成的数列\(\{b_{n}\}\)满足\(b_{n+1} > b_{n}\),\(n=1\),\(2\),\(…\),其中\( \overrightarrow{j}\)为方向与\(y\)轴正方向相同的单位向量,则称\(\{A_{n}\}\)为\(T\)点列\(.\)有下列说法
              \(①A_{1}(1,1),A_{2}(2, \dfrac {1}{2}),A_{3}(3, \dfrac {1}{3}),…,A_{n}(n. \dfrac {1}{n}),…\),为\(T\)点列;
              \(②\)若\(\{A_{n}\}\)为\(T\)点列,且点\(A_{2}\)在点\(A_{1}\)的右上方\(.\)任取其中连续三点\(A_{k}\)、\(A_{k+1}\)、\(A_{k+2}\),则\(\triangle A_{k}A_{k+1}A_{k+2}\)可以为锐角三角形;
              \(③\)若\(\{A_{n}\}\)为\(T\)点列,正整数若\(1\leqslant m < n < p < q\),满足\(m+q=n+p\),则\(a_{q}-a_{p}\geqslant (q-p)b_{p}\);
              \(④\)若\(\{A_{n}\}\)为\(T\)点列,正整数若\(1\leqslant m < n < p < q\),满足\(m+q=n+p\),则\( \overrightarrow{A_{n}A_{q}}\cdot \overrightarrow{j} > \overrightarrow{A_{m}A_{p}}\cdot \overrightarrow{j}\).
              其中,正确说法的个数为\((\)  \()\)
              A.\(1\)
              B.\(2\)
              C.\(3\)
              D.\(4\)
            • 4.

              两个大小相等的共点力\(F_{1}\),\(F_{2}\),当它们夹角为\(120^{\circ}\)时,合力大小为\(3\sqrt{2}N\),则当它们夹角为\(90^{\circ}\)时,合力大小为

              A.\(3\sqrt{2}N\)
              B.\(6N\)
              C.\(\dfrac{3\sqrt{6}}{2}N\)
              D.\(3\sqrt{6}N\)
            • 5. 一物体在力\( \overrightarrow{F_{1}}=(3,-4), \overrightarrow{F_{2}}=(2,-5), \overrightarrow{F_{3}}=(3,1)\)的共同作用下从点\(A(1,1)\)移动到点\(B(0,5).\)在这个过程中三个力的合力所做的功等于 ______ .
            • 6. 已知\(F=(2,3)\)作用一物体,使物体从\(A(2,0)\)移动到\(B(4,0)\),则力\(F\)对物体作的功为 ______
            • 7. 一艘船从\(A\)点出发以\(2 \sqrt {3}km/h\)的速度向垂直于对岸的方向行驶,同时河水的流速为\(2km/h\),求船实际航行速度的大小与方向\((\)用与流速间的夹角表示\()\).
            • 8.
              已知两个力\( \overrightarrow{F}_{1}, \overrightarrow{F}_{2}\)的夹角为\(90^{\circ}\),它们的合力大小为\(10N\),合力与\( \overrightarrow{F}_{1}\)的夹角为\(60^{\circ}\),那么\( \overrightarrow{F}_{2}\)的大小为\((\)  \()\)
              A.\(5 \sqrt {3}N\)
              B.\(5N\)
              C.\(10N\)
              D.\(5 \sqrt {2}N\)
            • 9.

              点\(P\)在平面上作匀速直线运动,速度\(v=(4,-3)\),设开始时点\(P\)的坐标为\((-10,10)\),则\(5\)秒后点\(P\)的坐标为\((\)速度单位:\(m/s\),长度单位:\(m)\)(    )

              A.\((-2,4)\)         
              B.\((-30,25)\)   
              C.\((10,-5)\)      
              D.\((5,-10)\)
            • 10.

              一条宽为\(\sqrt{3}km\)的河,水流速度为\(2km/h\),在河两岸有两个码头\(A\)、\(B\),已知\(AB=\sqrt{3}km\),船的最大航速为\(4km/h\),问该船从\(A\)码头到\(B\)码头怎样安排航行速度可使它最快到达彼岸\(B\)码头?用时多少?

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