PAS MATEMATIKA BLOG: Contoh 2 Vektor

$\begin{array}{ll} 6. & Diketahui titik P (n, 2), Q (1, - 2), n > 0 \\ dan panjang \overset{―}{P Q} = 5, maka nilai n \\ adalah . . . . \\ a . 1 \\ b . 2 \\ c . 3 \\ d . 4 \\ e . 5 \\ Jawab \\ \begin{aligned} \overset{―}{P Q} & = 5 \\ \sqrt{(x_{Q} - x_{P})^{2} + (y_{Q} - y_{P})^{2}} & = 5 \\ (x_{Q} - x_{P})^{2} + (y_{Q} - y_{P})^{2} & = 25 \\ (1 - n)^{2} + (- 2 - 2)^{2} & = 25 \\ (1 - n)^{2} + 16 & = 25 \\ (1 - n)^{2} - 3^{2} & = 0 \\ (1 + 3 - n) (1 - 3 - n) & = 0 \\ n = 4 atau n = - 2 \end{aligned} \end{array}$

$\begin{array}{ll} 7. & Diketahui vektor \vec{u} = (\begin{array}{c} 3 \\ 4 \end{array}) dan \vec{v} = (\begin{array}{c} 2 \\ - 1 \end{array}) . \\ Nilai | \vec{u} + \vec{v} | adalah . . . . \\ a . \sqrt{28} \\ b . \sqrt{30} \\ c . \sqrt{34} \\ d . \sqrt{44} \\ e . \sqrt{50} \\ Jawab \\ \begin{aligned} \vec{u} + \vec{v} & = (\begin{array}{c} 3 \\ 4 \end{array}) + (\begin{array}{c} 2 \\ - 1 \end{array}) \\ = (\begin{array}{c} 3 + 2 \\ 4 + (- 1) \end{array}) \\ = (\begin{array}{c} 5 \\ 3 \end{array}) \\ | \vec{u} + \vec{v} | & = \sqrt{5^{2} + 3^{2}} \\ = \sqrt{25 + 9} \\ = \sqrt{34} \end{aligned} \end{array}$

$\begin{array}{ll} 8. & Vektor satuan \vec{u} = (\begin{array}{c} - 5 \\ - 12 \end{array}) adalah . . . . \\ a . - \frac{1}{13} (\begin{array}{c} 5 \\ 12 \end{array}) \\ b . \frac{1}{15} (\begin{array}{c} - 5 \\ - 12 \end{array}) \\ c . - \frac{1}{17} (\begin{array}{c} 5 \\ 12 \end{array}) \\ d . - \frac{1}{17} (\begin{array}{c} 5 \\ 12 \end{array}) \\ e . \frac{1}{2} (\begin{array}{c} 5 \\ 12 \end{array}) \\ Jawab \\ \begin{aligned} {\vec{e}}_{\vec{u}} & = \frac{\vec{u}}{| \vec{u} |}, maka \\ {\vec{e}}_{(\begin{array}{c} - 5 \\ - 12 \end{array})} & = \frac{(\begin{array}{c} - 5 \\ - 12 \end{array})}{| (\begin{array}{c} - 5 \\ - 12 \end{array}) |} \\ = \frac{(\begin{array}{c} - 5 \\ - 12 \end{array})}{\sqrt{(- 5)^{2} + (- 12)^{2}}} \\ = \frac{- (\begin{array}{c} 5 \\ 12 \end{array})}{\sqrt{169}} \\ = - \frac{1}{13} (\begin{array}{c} 5 \\ 12 \end{array}) \end{aligned} \end{array}$

$\begin{array}{ll} 9. & Jika vektor \vec{p} = (\begin{array}{c} 8 \\ 7 \end{array}) dan \vec{q} = (\begin{array}{c} - 3 \\ 9 \end{array}) \\ Hasil dari \vec{p} + \vec{q} adalah . . . . \\ a . (\begin{array}{c} 6 \\ 14 \end{array}) \\ b . (\begin{array}{c} 6 \\ 13 \end{array}) \\ c . (\begin{array}{c} 6 \\ 15 \end{array}) \\ d . (\begin{array}{c} 5 \\ 16 \end{array}) \\ e . (\begin{array}{c} 5 \\ 48 \end{array}) \\ Jawab \\ \begin{aligned} \vec{p} + \vec{q} & = (\begin{array}{c} 8 \\ 7 \end{array}) + (\begin{array}{c} - 3 \\ 9 \end{array}) \\ = (\begin{array}{c} 8 - 3 \\ 7 + 9 \end{array}) \\ = (\begin{array}{c} 5 \\ 16 \end{array}) \end{aligned} \end{array}$

$\begin{array}{ll} 10. & Jika vektor \vec{p} = (\begin{array}{c} ^{2} \log 32 \\ -^{3} \log \frac{1}{81} \end{array}) dan \vec{q} = (\begin{array}{c} - 9 \\ - 21 \end{array}) \\ Hasil dari \vec{p} + \vec{q} adalah . . . . \\ a . (\begin{array}{c} 6 \\ 17 \end{array}) \\ b . (\begin{array}{c} - 6 \\ - 17 \end{array}) \\ c . (\begin{array}{c} 4 \\ 17 \end{array}) \\ d . (\begin{array}{c} - 4 \\ - 17 \end{array}) \\ e . (\begin{array}{c} 5 \\ - 16 \end{array}) \\ Jawab \\ \begin{aligned} \vec{p} + \vec{q} & = (\begin{array}{c} ^{2} \log 32 \\ -^{3} \log \frac{1}{81} \end{array}) + (\begin{array}{c} - 9 \\ - 21 \end{array}) \\ = (\begin{array}{c} 5 - 9 \\ 4 - 21 \end{array}) \\ = (\begin{array}{c} - 4 \\ - 17 \end{array}) \end{aligned} \end{array}$

PAS MATEMATIKA BLOG

Contoh 2 Vektor

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