ans

018511
$(\dfrac{x_1+\lambda x_2}{1+\lambda},\dfrac{y_1+\lambda y_2}{1+\lambda})$

018516
$(\dfrac{4}{5},\dfrac{3}{5})$处

018517
分别约为$101.5\text{N}$与$143.5\text{N}$

009638
$9$

009640
$(0,15)$

009641
(1) $\overrightarrow{f_2}=(1+\sqrt{3},3+\sqrt{3})$; (2) $30+10\sqrt{3}\text{J}$

009642
$(\dfrac{8}{37},\dfrac{85}{37})$

018519
$-\dfrac{\overrightarrow{a}\cdot\overrightarrow{c}+\overrightarrow{b}\cdot\overrightarrow{d}}{\overrightarrow{a}^2+\overrightarrow{c}^2}$

018520
$-\dfrac{5}{9}$

018526
当且仅当$\theta=0$时, $\overrightarrow{BP}\cdot \overrightarrow{CQ}$的值最大, 最大值为$0$

018527
(1) 是定值(定值为$1$), 理由略; (2) $3$


ans

040738
$-3$

040739
$\dfrac{\pi}{2}$

024816
$\dfrac{1}{2}\overrightarrow{e_1}$

040741
$(-5,-5)$

040742
$[0,2]$

040743
$(-\dfrac{7}{9},-\dfrac{7}{3})$

040744
$11$或$-2$

040747
$(-\infty,-4)\cup (-4,1)$

040746
$\sqrt{3}$

040749
$[\dfrac{1}{2},1]$

024815
$1-\sqrt{2}$

040751
$\arccos\dfrac{1}{7}$

024788
$\dfrac{3}{11}$

024789
\textcircled{3}\textcircled{4}

024790
D

024791
$\overrightarrow{a}=-\sqrt{3}\overrightarrow{b}-\dfrac{1}{3}\overrightarrow{c}$

017646
$\dfrac{19}{18}$

024792
$\dfrac{3}{8}\overrightarrow{a}+\dfrac{1}{4}\overrightarrow{b}$

024793
$-\dfrac{11}{16}$

010002
(1) $\arccos\dfrac{13}{14}$; (2) $28\sqrt{74}$