12. Diketahui vektor overline u =( matrix 4\\ -2 matrix )dan overline v =( matrix -1\\ 3 matrix ) sudut antara ü tan overline v adalah...
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Jawab:
vektor
sudut dua vektor (α)
[tex]\sf \overline u= \binom{4}{-2}~ ~ dan ~ \overline v = \binom{-1}{3}[/tex]
|u|= √(4²+(-2)²) = √20
|v| = √((-1)² + (3)²) = √10
|u|. |v| = √200 = 10√2
u.v = 4(-1) - 2(3)
u.v = -4- 6 = -10
[tex]\sf cos(u,v) = \dfrac{u.v}{|u|v|}[/tex]
[tex]\sf cos(\alpha) = \dfrac{-10}{10\sqrt {2}}= -\frac{1}{2}\sqrt 2[/tex]
cos α = - ¹/₂√2 = - cos 45
α = 180 - 45
α = 135°
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