\(\overrightarrow{u}=4\overrightarrow{MA}-3\left(\overrightarrow{MA}+\overrightarrow{AB}\right)+\overrightarrow{MA}+\overrightarrow{AC}-2\left(\overrightarrow{MA}+\overrightarrow{AD}\right)\)

\(=-3\overrightarrow{AB}+\overrightarrow{AC}-2\overrightarrow{AD}=-3\left(\overrightarrow{AB}+\overrightarrow{AD}\right)+\overrightarrow{AC}+\overrightarrow{AD}\)

\(=-3\overrightarrow{AC}+\overrightarrow{AC}+\overrightarrow{AD}=-2\overrightarrow{AC}+\overrightarrow{AD}\)

\(\overrightarrow{u}^2=\left(-2\overrightarrow{AC}+\overrightarrow{AD}\right)^2=4AC^2-4\overrightarrow{AC}.\overrightarrow{AD}+AD^2\)

\(=4\left(a\sqrt{2}\right)^2-4.a\sqrt{2}.a.cos45^0+a^2=5a^2\)

\(\Rightarrow\left|\overrightarrow{u}\right|=a\sqrt{5}\)

Câu 44: C

Câu 45: C

41. Roger: " I don't believe it. " - Anita: " ..................... "

→ Đáp án:                C. Neither do I   

42. Jill : " Do you know Lisa's an excellent pianist ? - Maria: " ..................... "

→ Đáp án:                B. Yes, she does 

43. Karen: " ............... this word in English ? " - Betsy: " C-O-Z-Y "

→ Đáp án:                B. How do you spell    

44. Customer: " I think my change is wrong. " - Shop assistant: " ................... "

→ Đáp án:                C. Sorry. I don't think I have any change  

45. Mandy: " I've got a toothache. " - George: " ................. " 

→ Đáp án:                D. Why don't you see the dentist ? 

giúp mình

D

D

d 

Sao lại = ... hả bạn? Nếu $35\times x+45$ không có giá trị nào thì cũng không tìm được $x$ nhé.

chữ đã đẹp còn mờ nữa :))

Do \(M\in d\) nên M(1+2t; 1-t ; t) 

MA+MB= \(\sqrt{4t^2+\left(t-1\right)^2+\left(t+1\right)^2}+\sqrt{\left(2t-1\right)^2+t^2+\left(t-1\right)^2}\)

\(=\sqrt{6t^2+2}+\sqrt{6t^2-6t+2}=\sqrt{6t^2+2+}\sqrt{6.\left(t-\dfrac{1}{2}\right)^2+\dfrac{1}{2}}\) 

Chọn \(\overset{r}{u}=\left(\sqrt{6t};\sqrt{2}\right);\overset{r}{v}=\left(\sqrt{6}.\left(\dfrac{1}{2}-t\right);\dfrac{1}{\sqrt{2}}\right)\)

\(\Rightarrow\overset{r}{u}+\overset{r}{v}=\left(\dfrac{\sqrt{6}}{2};\dfrac{3}{\sqrt{2}}\right)\) , Ta có :

MA+MB=\(\left|\overset{r}{u}\right|+\left|\overset{r}{v}\right|\ge\left|\overset{r}{u}+\overset{r}{v}\right|=\sqrt{\dfrac{6}{4}+\dfrac{9}{2}}=\sqrt{6}\)

Dấu đẳng thức xảy ra <=> \(\overset{r}{u};\overset{r}{v}\) cùng hướng

\(\Leftrightarrow\dfrac{\sqrt{6t}}{\sqrt{6}\left(\dfrac{1}{2}-t\right)}=\dfrac{\sqrt{2}}{\dfrac{1}{\sqrt{2}}}\Leftrightarrow1=1-2t\)

\(\Leftrightarrow t=\dfrac{1}{3}\) . Vậy MA+MB nhỏ nhất

\(\Leftrightarrow M\left(\dfrac{5}{3},\dfrac{2}{3};\dfrac{1}{3}\right)\)

Vậy chọn D