Cho hình chữ nhật ABCD có tâm O và AB= a AD =2a . Dựng và tính độ dài các véc tơ
1) 2AO - BC
2) OC + 2AB
3) 3AB + 2OD
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ABCD là hình chữ nhật
=>AC cắt BD tại trung điểm của mỗi đường và AC=BD
=>O là trung điểm chung của AC và BD
ABCD là hình chữ nhật
=>AB=CD=2a; BC=AD
O là trung điểm của AC
=>\(AC=2\cdot AO=2a\cdot\sqrt{5}\)
=>\(BD=2a\sqrt{5}\)
ABCD là hình chữ nhật
=>ΔABC vuông tại B
=>\(BA^2+BC^2=AC^2\)
=>\(BC^2=AC^2-AB^2=\left(2a\sqrt{5}\right)^2-\left(2a\right)^2=20a^2-4a^2=16a^2\)
=>BC=4a
=>\(\left|\overrightarrow{BC}\right|=4a\)
\(\left|\overrightarrow{AB}-\overrightarrow{BC}\right|=\left|\overrightarrow{AB}+\overrightarrow{CB}\right|=BD=a\sqrt{6}\)
\(\left|\overrightarrow{AB}+\overrightarrow{AD}\right|=a\sqrt{5}\)
\(\left|\overrightarrow{BC}-\overrightarrow{OD}\right|=\left|\overrightarrow{AD}+\overrightarrow{DO}\right|=AO=\dfrac{a\sqrt{5}}{2}\)
a) \(AC = BD = \sqrt {A{B^2} + A{D^2}} \\= \sqrt {{{\left( {2a} \right)}^2} + {a^2}} = a\sqrt 5 \)
\(\cos \left( {\overrightarrow {AB} ,\overrightarrow {AO} } \right) = \cos \widehat {OAB} =\\ \cos \widehat {CAB} = \frac{{AB}}{{AC}} = \frac{{2a}}{{a\sqrt 5 }} = \frac{{2\sqrt 5 }}{5}\)
\(\begin{array}{l}\overrightarrow {AB} .\overrightarrow {AO} = \left| {\overrightarrow {AB} } \right|.\left| {\overrightarrow {AO} } \right|.\cos \left( {\overrightarrow {AB} ,\overrightarrow {AO} } \right) \\= AB.\frac{1}{2}AC.\cos \left( {\overrightarrow {AB} ,\overrightarrow {AO} } \right)\\ = 2a.\frac{1}{2}.a\sqrt 5 .\frac{{2\sqrt 5 }}{5} = 2{a^2}\end{array}\)
b) \(AB \bot AD \Rightarrow \left( {\overrightarrow {AB} ,\overrightarrow {AD} } \right) = 90^o \Rightarrow \cos \left( {\overrightarrow {AB} ,\overrightarrow {AD} } \right) =0 \Rightarrow \overrightarrow {AB} .\overrightarrow {AD} = 0\)
a) \(S_{ABCD}=AB.AD=20,4.18,5=377,4cm^2\)
b) Mình xin sửa lại giao điểm của MN và DC là E nha--> giờ ta tính CE
Xét 2 tam giác MNB và tam giác ENC có:
\(\widehat{MBN}=\widehat{ECN}=90^0\)
\(NB=NC\)(Vì N trung điểm BC)
\(\widehat{MNB}=\widehat{ENC}\)(2 góc đối đỉnh)
\(\Rightarrow\Delta MNB=\Delta ENC\left(g.c.g\right)\Rightarrow CE=BM=\frac{1}{2}AB=\frac{20,4}{2}=10,2cm\)
Lời giải:
1.
$\overrightarrow{2AO}-\overrightarrow{BC}=\overrightarrow{AC}-\overrightarrow{BC}=\overrightarrow{AB}$
Độ dài: $|\overrightarrow{AB}|=a$
2.
Trên tia đối của $AC$ lấy $T$ sao cho $TA=OC$
Trên tia đối của $BA$ lấy $K$ sao cho $BA=BK$
$\overrightarrow{OC}+2\overrightarrow{AB}=\overrightarrow{TA}+\overrightarrow{AB}+\overrightarrow{AB}$
$=\overrightarrow{TB}+\overrightarrow{AB}$
$=\overrightarrow{TB}+\overrightarrow{BK}=\overrightarrow{TK}$
Ta có:
$TC=3OC=\frac{3}{2}AC=\frac{3}{2}\sqrt{(2a)^2+a^2}=\frac{3\sqrt{5}}{2}a$
$CK=\sqrt{BC^2+BK^2}=\sqrt{(2a)^2+a^2}=\sqrt{5}a$
$\cos \widehat{TCK}=\cos 2\widehat{TCB}=2\cos^2 \widehat{TCB}-1$
$=2(\frac{CB}{AC})^2-1=\frac{3}{5}$
Áp dụng định lý cos:
$TK^2=TC^2+CK^2-2TC.CK\cos \widehat{TCK}$
$=\frac{45}{4}a^2+5a^2-9a^2=\frac{29}{4}a^2$
$\Rightarrow TK=\frac{\sqrt{29}}{2}a$
3. Trên tia đối tia $CD$ lấy $M$ sao cho $CM=CD$
$3\overrightarrow{AB}+2\overrightarrow{OD}=3\overrightarrow{DC}+2\overrightarrow{OD}=2\overrightarrow{OC}+\overrightarrow{DC}$
$=\overrightarrow{AC}+\overrightarrow{DC}=\overrightarrow{AC}+\overrightarrow{CM}=\overrightarrow{AM}$
$AM=\sqrt{AD^2+DM^2}=\sqrt{(2a)^2+(2a)^2}=2\sqrt{2}a$
Hình vẽ:
![](data:image/png;base64,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)