Długość wektora o danych współrzędnych [tex]\vec{AB} =[x, y][/tex] obliczamy ze wzoru:
[tex]|\vec AB| = \sqrt{x^{2}+y^{2}}[/tex]
[tex]a) \ \vec u = [-15,11] \ \ \rightarrow \ \ x = -5, \ y = 11\\\\|\vec{u}| = \sqrt{(-5)^{2}+11^{2}} =\sqrt{25+121} = \sqrt{169} = \underline{13}[/tex]
[tex]b) \ \vec{v} = [4\frac{1}2},6] \ \ \rightarrow \ \ x = 4\frac{1}{2} = 4,5, \ y = 6\\\\|\vec{v}| = \sqrt{4,5^{2}+6^{2}} = \sqrt{20,25+36} = \sqrt{56,25} = \underline{7,5}[/tex]
[tex]c) \ \vec{p} = [-11, -60] \ \ \rightarrow \ \ x = -11, \ y = -60\\\\|\vec{p}| = \sqrt{(-11)^{2}+(-60)^{2}} = \sqrt{121+3600} = \sqrt{3721} = \underline{61}[/tex]
[tex]d) \ \vec{s} = [2, -\sqrt{5}] \ \ \rightarrow \ \ x = 2, \ y = -\sqrt{5}\\\\|\vec{s}| = \sqrt{2^{2}+(-\sqrt{5})^{2}} = \sqrt{4+5} = \sqrt{9} = \underline{3}[/tex]
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[tex]\huge\boxed{a) \ |\vec{u}| = 13}\\\\\\\huge\boxed{ b) \ |\vec{v}| = 7,5} \\\\\\\huge\boxed{c) \ |{\vec{p}| = 61}}\\\\\\\huge\boxed{d) \ |\vec{s}| = 3}[/tex]
WEKTOR
Długość wektora o danych współrzędnych [tex]\vec{AB} =[x, y][/tex] obliczamy ze wzoru:
[tex]|\vec AB| = \sqrt{x^{2}+y^{2}}[/tex]
[tex]a) \ \vec u = [-15,11] \ \ \rightarrow \ \ x = -5, \ y = 11\\\\|\vec{u}| = \sqrt{(-5)^{2}+11^{2}} =\sqrt{25+121} = \sqrt{169} = \underline{13}[/tex]
[tex]b) \ \vec{v} = [4\frac{1}2},6] \ \ \rightarrow \ \ x = 4\frac{1}{2} = 4,5, \ y = 6\\\\|\vec{v}| = \sqrt{4,5^{2}+6^{2}} = \sqrt{20,25+36} = \sqrt{56,25} = \underline{7,5}[/tex]
[tex]c) \ \vec{p} = [-11, -60] \ \ \rightarrow \ \ x = -11, \ y = -60\\\\|\vec{p}| = \sqrt{(-11)^{2}+(-60)^{2}} = \sqrt{121+3600} = \sqrt{3721} = \underline{61}[/tex]
[tex]d) \ \vec{s} = [2, -\sqrt{5}] \ \ \rightarrow \ \ x = 2, \ y = -\sqrt{5}\\\\|\vec{s}| = \sqrt{2^{2}+(-\sqrt{5})^{2}} = \sqrt{4+5} = \sqrt{9} = \underline{3}[/tex]