Jawab:
a. [tex]\sqrt{83}[/tex]
b. [tex]\sqrt{17} + \sqrt{26}[/tex]
c. 4[tex]\sqrt{17}[/tex]
d. [tex]\sqrt{499}[/tex]
Penjelasan dengan langkah-langkah:
a. u + v = ( 2+1, -2-3, 3+4) = (3,-5,7)
maka panjang u+v = |u+v| = [tex]\sqrt{{3^{2}}+{(-5^{2})}+{7^{2}}} = \sqrt{9+25+49} = \sqrt{83}[/tex]
b. |u| = [tex]\sqrt{{2^{2}}+{(-2^{2})}+{3^2}} = \sqrt{4+4+9}=\sqrt{17}[/tex]
|v| = [tex]\sqrt{1^2+{(-3^2)+4^2}} = \sqrt{1+9+16} = \sqrt{26}[/tex]
|u| + |v| = [tex]\sqrt{17} + \sqrt{26}[/tex]
c. -2u = -2 x (2, -2, 3) = (-4, 4, -6)
|-2u| = [tex]\sqrt{(-4^2)+4^2+(-6^2)} = \sqrt{16+16+36} = \sqrt{68}[/tex]
|-2u| + 2|u| = [tex]\sqrt{68}+2\sqrt{17}= \sqrt{17x4} + 2\sqrt{17} = 2\sqrt{17} + 2\sqrt{17} = 4\sqrt{17}[/tex]
d. 3u = 3 x (2, -2, 3) = (6, -6, 9)
-5v = -5 x (1, -3, 4) = (-2, 15, -20)
3u -5v + w = (6, -6, 9) + (-2, 15, -20) + (3, 6, -4) = (7, 15, -15)
|3u-5v+w| = [tex]\sqrt{7^2+15^2+(-15^2)} = \sqrt{49+225+225} = \sqrt{499}[/tex]
[answer.2.content]
