Bài 106516

Question

Tìm góc của 2 vectơ:
a. $\overrightarrow{a}=(4;3), \overrightarrow{b}=(1;7)$
b. $\overrightarrow{a}=(2;5), \overrightarrow{b}=(3;-7)$
c. $\overrightarrow{a}=(6;-8), \overrightarrow{b}=(12;9)$
d. $\overrightarrow{a}=(2;-6), \overrightarrow{b}=(-3;9)$

phuongna · Answer 1 · 6/1/2012 4:58:09 PM

a) $\cos (\overrightarrow{a}, \overrightarrow{b})=\frac{\mathrm{\overrightarrow{a}. } \overrightarrow{b} }{\mathrm|{\overrightarrow{a}| .} |\overrightarrow{b} |}=\frac{\mathrm{4}+21 }{\mathrm{\sqrt{4^2+3^2}}. \sqrt{1^2+7^2}}=\frac{25}{25\sqrt{2}} =\frac{1}{\sqrt{2}} $
$\Rightarrow (\overrightarrow{a}, \overrightarrow{b})=45^\circ $.
b) $\cos (\overrightarrow{a}, \overrightarrow{b})=\frac{\overrightarrow{a}.\overrightarrow{b} }{|\overrightarrow{a}|. |\overrightarrow{b}| } =\frac{\mathrm{6+} (-35)}{\mathrm{\sqrt{2^2+5^2}.} \sqrt{3^2+(-7)^2}} =\frac{-29}{\sqrt{29}.\sqrt{58}}=-\frac{1}{\sqrt{2}} $
Vậy $\cos ( \overrightarrow{a}, \overrightarrow{b} )=-\cos 45^\circ=\cos(180^\circ-45^\circ)\Rightarrow (\overrightarrow{a}, \overrightarrow{b})=135^\circ. $
c) $\cos( \overrightarrow{a}, \overrightarrow{b})=\frac{72-72}{\sqrt{36+64}.\sqrt{144+81}}=0\Rightarrow (\overrightarrow{a}, \overrightarrow{b})=90^\circ $.
d) $\cos(\overrightarrow{a} ,\overrightarrow{b})=\frac{-6-54}{\sqrt{4+36}.\sqrt{\sqrt{9+81}}}= \frac{-60}{\sqrt{40}.\sqrt{90}}=-1 $
$(\overrightarrow{a}, \overrightarrow{b})=180^\circ $.

Bài 106516

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Bài 106516

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