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Ta có:
\(\overrightarrow{AM}=\dfrac{1}{2}\left(\overrightarrow{AO}+\overrightarrow{AB}\right)\)
\(\Leftrightarrow\overrightarrow{AM}=\dfrac{1}{2}\left(\overrightarrow{AO}+\overrightarrow{AO}+\overrightarrow{OB}\right)\)
\(\Leftrightarrow\overrightarrow{AM}=\dfrac{1}{2}\left(2\overrightarrow{AO}+\overrightarrow{OB}\right)\)
\(\Leftrightarrow\overrightarrow{AM}=\overrightarrow{AO}+\dfrac{1}{2}\overrightarrow{OB}\)
\(\Leftrightarrow\overrightarrow{AM}=\dfrac{1}{2}\overrightarrow{OB}-\overrightarrow{OA}\)
\(\RightarrowĐPCM\)
Câu b ) Bạn làm tương tự câu a , ta có vecto BN = 1/2 (BO +BC ) , rồi là như câu a
chúc bạn hok tốt
a: \(\overrightarrow{AM}+\overrightarrow{BN}=\dfrac{1}{2}\overrightarrow{AB}+\dfrac{1}{2}\overrightarrow{BC}=\dfrac{1}{2}\overrightarrow{AC}\)
b: \(=\dfrac{1}{2}\overrightarrow{AC}+\dfrac{1}{2}\overrightarrow{AC}+\dfrac{1}{2}\overrightarrow{BA}\)
\(=\overrightarrow{AC}+\dfrac{1}{2}\overrightarrow{BA}\)
c: \(\overrightarrow{AM}+\overrightarrow{BN}+\overrightarrow{CP}\)
\(=\dfrac{1}{2}\overrightarrow{AB}+\dfrac{1}{2}\overrightarrow{BC}+\dfrac{1}{2}\overrightarrow{CA}\)
\(=\dfrac{1}{2}\left(\overrightarrow{AC}+\overrightarrow{CA}\right)=\overrightarrow{0}\)
\(3\overrightarrow{AC}=2\overrightarrow{CB}\leftrightarrow3\overrightarrow{AO}+3\overrightarrow{OC}=2\overrightarrow{CO}+2\overrightarrow{OB}\)
\(\rightarrow5\overrightarrow{OC}=3\overrightarrow{OA}+2\overrightarrow{OB}\)
\(\rightarrow\overrightarrow{OC}=\dfrac{3}{5}\overrightarrow{OA}+\dfrac{2}{5}\overrightarrow{OB}\)
câu 2 ( các kí hiệu vecto khi lm bài thỳ b tự viết nhé mk k viết kí hiệu để trả lời cho nhanh hỳ hỳ )
OA+ OB + OC = OA'+ OB' + OC'
<=> OA - OA' + OB - OB' + OC - OC' = 0
<=> A'A + B'B + C'C = 0
<=> 2 ( BA + CB + AC ) = 0
<=> 2 ( CB + BA + AC ) = 0
<=> 2 ( CA + AC ) = 0
<=> 0 = 0 ( luôn đúng )
câu 1 ( các kí hiệu vecto b cx tự viết nhá )
VT = OD + OC = OA + AD + OB + BC = OA + OB + AD + BC = BO + OB + AD + BC = 0 + AD + BC = AD + BC = VP ( đpcm)
a/ \(\left|\overrightarrow{OA}+\overrightarrow{OC}+\overrightarrow{OB}+\overrightarrow{OD}\right|=\left|\overrightarrow{0}+\overrightarrow{0}\right|=0\)
b/ \(\left|\overrightarrow{OA}+\overrightarrow{OB}\right|+\left|\overrightarrow{OC}+\overrightarrow{OD}\right|=a+a=2a\)
c/
\(\left|\overrightarrow{OA}+\overrightarrow{OC}+\overrightarrow{OB}\right|+\left|\overrightarrow{OD}\right|=\left|\overrightarrow{OB}\right|+\left|\overrightarrow{OD}\right|=2\left|\overrightarrow{OB}\right|=2\sqrt{a^2-\frac{a^2}{4}}=a\sqrt{3}\)
a)Ta có:
\(\overrightarrow{OA}+\overrightarrow{OM}+\overrightarrow{ON}=\overrightarrow{CO}+\dfrac{1}{2}\left(\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OC}+\overrightarrow{OD}\right)\)
\(=\overrightarrow{CO}+\dfrac{1}{2}.2\overrightarrow{OC}\)
\(=\overrightarrow{0}\)
\(\RightarrowĐPCM\)
b) Ta có:
\(\overrightarrow{AM}=\dfrac{1}{2}\left(\overrightarrow{AD}+2\overrightarrow{AB}\right)\)
\(\Rightarrow2\overrightarrow{AM}=\overrightarrow{AD}+2\overrightarrow{AB}\) (1)
Mà \(2\overrightarrow{AM}=\overrightarrow{AB}+\overrightarrow{AC}\)(2)
Từ (1)(2) =>\(\overrightarrow{AD}+2\overrightarrow{AB}=\overrightarrow{AB}+\overrightarrow{AC}\)
\(\Rightarrow\overrightarrow{AC}+\overrightarrow{AB}=\overrightarrow{AB}+\overrightarrow{AC}\)
\(\RightarrowĐPCM\)