a) Ta có: \(\left\{ \begin{array}{l}AD//BC\\AD = BC\end{array} \right.\) (do tứ giác ABCD là hình bình hành)

\( \Rightarrow \overrightarrow {AD}  = \overrightarrow {BC} \)

b) Ta có: \(\overrightarrow {AB}  + \overrightarrow {AD}  = \overrightarrow {AB}  + \overrightarrow {BC}  = \overrightarrow {AC} \)

\(\overrightarrow{NC}=2\overrightarrow{ND}=2\overrightarrow{NC}+2\overrightarrow{CD}\Rightarrow\overrightarrow{NC}=2\overrightarrow{DC}\Rightarrow\overrightarrow{CN}=2\overrightarrow{CD}\)

a.

\(\overrightarrow{DM}=\overrightarrow{DC}+\overrightarrow{CM}=\overrightarrow{AB}+\dfrac{1}{2}\overrightarrow{CB}=\overrightarrow{AB}-\dfrac{1}{2}\overrightarrow{AD}\)

\(\overrightarrow{MN}=\overrightarrow{MC}+\overrightarrow{CN}=\dfrac{1}{2}\overrightarrow{BC}+2\overrightarrow{CD}=-2\overrightarrow{AB}+\dfrac{1}{2}\overrightarrow{AD}\)

b.

\(\left\{{}\begin{matrix}\overrightarrow{AC}=\overrightarrow{AB}+\overrightarrow{AD}\\\overrightarrow{BD}=\overrightarrow{BA}+\overrightarrow{AD}=-\overrightarrow{AB}+\overrightarrow{AD}\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\overrightarrow{AB}=\dfrac{1}{2}\overrightarrow{AC}-\dfrac{1}{2}\overrightarrow{BD}\\\overrightarrow{AD}=\dfrac{1}{2}\overrightarrow{AC}+\dfrac{1}{2}\overrightarrow{BD}\end{matrix}\right.\)

\(\Rightarrow\overrightarrow{MN}=-2\left(\dfrac{1}{2}\overrightarrow{AC}-\dfrac{1}{2}\overrightarrow{BD}\right)+\dfrac{1}{2}\left(\dfrac{1}{2}\overrightarrow{AC}+\dfrac{1}{2}\overrightarrow{BD}\right)=-\dfrac{3}{4}\overrightarrow{AB}+\dfrac{5}{4}\overrightarrow{BD}\)

1: ABCD là hình bình hành

=>\(\overrightarrow{DA}+\overrightarrow{DC}=\overrightarrow{DB}\)

\(\overrightarrow{AB}+\overrightarrow{DA}=\overrightarrow{DA}+\overrightarrow{AB}=\overrightarrow{DB}\)

2: \(\overrightarrow{AC}-\overrightarrow{ED}+\overrightarrow{CD}+\overrightarrow{EC}-\overrightarrow{BC}\)

\(=\overrightarrow{AC}+\overrightarrow{CD}+\overrightarrow{DE}+\overrightarrow{EC}+\overrightarrow{CB}\)

\(=\overrightarrow{AD}+\overrightarrow{DE}+\overrightarrow{EC}+\overrightarrow{CB}\)

\(=\overrightarrow{AE}+\overrightarrow{EC}+\overrightarrow{CB}=\overrightarrow{AC}+\overrightarrow{CB}=\overrightarrow{AB}\)

3:

a: \(\overrightarrow{BA}+\overrightarrow{DA}+\overrightarrow{AC}\)

\(=-\overrightarrow{AB}-\overrightarrow{AD}+\overrightarrow{AB}+\overrightarrow{AD}=\overrightarrow{0}\)

\(\overrightarrow{AB}+\overrightarrow{CA}+\overrightarrow{BC}\)

\(=\overrightarrow{CA}+\overrightarrow{AB}+\overrightarrow{BC}\)

\(=\overrightarrow{CB}+\overrightarrow{BC}=\overrightarrow{0}\)

Gọi H là trung điểm của BC

Xét ΔABC có AH là đường trung tuyến

nên \(\overrightarrow{AB}+\overrightarrow{AC}=2\cdot\overrightarrow{AH}\)

b: ABCD là hình vuông

=>\(DB^2=DA^2+AB^2\)

=>\(DB^2=a^2+a^2=2a^2\)

=>\(DB=a\sqrt2\)

ABCD là hình vuông

=>\(\overrightarrow{DA}+\overrightarrow{DC}=\overrightarrow{DB}\)

=>\(\left|\overrightarrow{DA}+\overrightarrow{DC}\right|=DB=a\sqrt2\)

\(\overrightarrow{AB}-\overrightarrow{CB}=\overrightarrow{AB}+\overrightarrow{BC}=\overrightarrow{AC}\)

=>\(\left|\overrightarrow{AB}-\overrightarrow{CB}\right|=CA=a\sqrt2\)

\(a,\overrightarrow{AB}-\overrightarrow{DA}+\overrightarrow{CD}=\overrightarrow{AD}+\overrightarrow{AB}+\overrightarrow{CD}=\overrightarrow{AD}+\overrightarrow{0}=\overrightarrow{AD}\)

\(b,\overrightarrow{AM}=\dfrac{\overrightarrow{AO}+\overrightarrow{AB}}{2}=\dfrac{\overrightarrow{AB}}{2}+\dfrac{\dfrac{1}{2}\overrightarrow{AC}}{2}=\overrightarrow{\dfrac{AB}{2}}+\dfrac{1}{4}\overrightarrow{AC}\)

\(=\overrightarrow{\dfrac{AB}{2}}+\dfrac{\overrightarrow{AB}+\overrightarrow{BC}}{4}=\dfrac{3}{4}\overrightarrow{AB}+\dfrac{\overrightarrow{BC}}{4}=\dfrac{1}{4}\overrightarrow{BC}+\dfrac{3}{4}\overrightarrow{AB}\left(1\right)\)

\(\overrightarrow{AN}=\overrightarrow{BN}-\overrightarrow{BA}=k.\overrightarrow{BC}+\overrightarrow{AB}\left(2\right)\)

\(\left(1\right)\left(2\right)A,M,N\) \(thẳng\) \(hàng\Leftrightarrow\dfrac{k}{\dfrac{1}{4}}=\dfrac{1}{\dfrac{3}{4}}\Leftrightarrow k=\dfrac{1}{3}\)

Chọn C

Kham khảo 

Câu hỏi của Khanh Quynh - Toán lớp 10 | Học trực tuyến

vào thống kê của mk , nhấn vào chữ màu xanh trog câu tl này sẽ ra 

Hc tốt 

toi la hai den nha toi toi chi cho

bài 1

a CO-OB=BA

<=.> CO = BA +OB

<=> CO=OA ( LUÔN ĐÚNG )=>ĐPCM

b AB-BC=DB

<=> AB=DB+BC

<=> AB=DC(LUÔN ĐÚNG )=> ĐPCM

Cc DA-DB=OD-OC

<=> DA+BD= OD+CO

<=> BA= CD (LUÔN ĐÚNG )=> ĐPCM

d DA-DB+DC=0

VT= DA +BD+DC

= BA+DC

Mà BA=CD(CMT)

=> VT= CD+DC=O

BÀI 2

AC=AB+BC

BD=BA+AD

=> AC+BD= AB+BC+BA+AD=BC+AD (đpcm)