PAS MATEMATIKA BLOG: Maret 2020

$\color{blue}\begin{array}{ll}\\ 1.&\textrm{Panjang vektor}\: \: \vec{g}=\begin{pmatrix} -4\\ -8 \end{pmatrix}\: \: \textrm{adalah}....\\ &\textrm{A}.\quad \displaystyle \sqrt{4}\\ &\textrm{B}.\quad \sqrt{12}\\ &\textrm{C}.\quad \sqrt{20}\\ &\textrm{D}.\quad \displaystyle \sqrt{80}\\ &\textrm{E}.\quad \sqrt{100}\\\\ &\textrm{Jawab}:\qquad \textbf{D}\\ &\begin{aligned}\vec{p}&=\begin{pmatrix} -4\\ -8 \end{pmatrix},\: \: \textrm{maka besar dari vektor}\: \: \vec{p}\: \: \textrm{adalah}=\left | \vec{p} \right |=\sqrt{x^{2}+y^{2}}\\ &\textrm{Yaitu}\\ \left | \vec{p} \right |&=\sqrt{(-4)^{2}+(-8)^{2}}\\ &=\sqrt{16+64}=\sqrt{80} \end{aligned} \end{array}$
$\color{blue}\begin{array}{ll}\\ 2.&\textrm{Vektor satuan dari}\: \: \vec{a}=3\vec{i}-4\vec{j}\: \: \textrm{adalah}....\\ &\textrm{A}.\quad \displaystyle \frac{4}{5}\vec{i}-\frac{3}{5}\vec{j}\\ &\textrm{B}.\quad \displaystyle \frac{3}{5}\vec{i}-\frac{4}{5}\vec{j}\\ &\textrm{C}.\quad 3\vec{i}-4\vec{j}\\ &\textrm{D}.\quad 4\vec{i}-3\vec{j}\\ &\textrm{E}.\quad 15\vec{i}-20\vec{j}\\\\ &\textrm{Jawab}:\qquad \textbf{B}\\ &\begin{aligned}\vec{a}&=3\vec{i}-4\vec{j}\\ &\textrm{Vektor satuan dari vektor}\: \: \vec{a}\: \: \textrm{adalah}\: :\: \hat{e}_{_{\vec{a}}}=\displaystyle \frac{1}{\left | \vec{a} \right |}. \vec{a}\\ &\textrm{Sehingga}\\ \hat{e}_{_{\vec{a}}}&=\displaystyle \frac{1}{\sqrt{3^{2}+(-4)^{2}}}.\begin{pmatrix} 3\\ -4 \end{pmatrix}\\ &=\displaystyle \frac{1}{5}\begin{pmatrix} 3\\ -4 \end{pmatrix}\\ &\textrm{atau dalam vektor basis}\\ &=\displaystyle \frac{3}{5}\vec{i}-\frac{4}{5}\vec{j} \end{aligned} \end{array}$
$\begin{array}{ll}\\ 3.&\textrm{Vektor berikut yang memiliki panjang}\: \: \sqrt{1013}\: \: \textrm{satuan adalah}....\\ &\textrm{A}.\quad \displaystyle 18\vec{i}-19\vec{j}\\ &\textrm{B}.\quad \displaystyle 19\vec{i}-20\vec{j}\\ &\textrm{C}.\quad 20\vec{i}-21\vec{j}\\ &\textrm{D}.\quad 21\vec{i}-22\vec{j}\\ &\textrm{E}.\quad 22\vec{i}-23\vec{j}\\\\ &\textrm{Jawab}:\qquad \textbf{E}\\ &\begin{aligned}\textrm{yang}&\: \: \textrm{paling mungkin adalah}\: : \: \\ &=\sqrt{22^{2}+23^{2}}=\sqrt{484+529}=\sqrt{1013}\end{aligned} \end{array}$
$\begin{array}{ll}\\ 4.&\textrm{Jika vektor}\: \: \vec{a}=\begin{pmatrix} 8\\ 7 \end{pmatrix}\: \: \textrm{dan}\: \: \vec{b}=\begin{pmatrix} -3\\ 9 \end{pmatrix}\: \: \textrm{Hasil dari}\: \: \vec{a}+\vec{b}\: \: \textrm{adalah}....\\ &\textrm{A}.\quad \begin{pmatrix} 6\\ 14 \end{pmatrix}\\ &\textrm{B}.\quad \begin{pmatrix} 6\\ 13 \end{pmatrix}\\ &\textrm{C}.\quad \begin{pmatrix} 6\\ 15 \end{pmatrix}\\ &\textrm{D}.\quad \begin{pmatrix} 5\\ 16 \end{pmatrix}\\ &\textrm{E}.\quad \begin{pmatrix} 5\\ 48 \end{pmatrix}\\\\ &\textrm{Jawab}:\qquad \textbf{D}\\ &\begin{aligned}\vec{a}+\vec{b}&=\begin{pmatrix} 8\\ 7 \end{pmatrix}+\begin{pmatrix} -3\\ 9 \end{pmatrix}\\ &=\begin{pmatrix} 8-3\\ 7+9 \end{pmatrix}\\ &=\begin{pmatrix} 5\\ 16 \end{pmatrix} \end{aligned} \end{array}$

$\begin{array}{ll}\\ 5.&\textrm{Jika vektor}\: \: \vec{u}=\begin{pmatrix} ^{2}\log 32\\ -\, ^{5}\log \displaystyle \frac{1}{625} \end{pmatrix}\: \: \textrm{dan}\: \: \vec{v}=\begin{pmatrix} -9\\ -21 \end{pmatrix}\: \: \textrm{Hasil dari}\: \: \vec{u}+\vec{v}\: \: \textrm{adalah}....\\ &\textrm{A}.\quad \begin{pmatrix} 6\\ 17 \end{pmatrix}\\ &\textrm{B}.\quad \begin{pmatrix} -6\\ -17 \end{pmatrix}\\ &\textrm{C}.\quad \begin{pmatrix} 4\\ 17 \end{pmatrix}\\ &\textrm{D}.\quad \begin{pmatrix} -4\\ -17 \end{pmatrix}\\ &\textrm{E}.\quad \begin{pmatrix} 5\\ -16 \end{pmatrix}\\\\ &\textrm{Jawab}:\qquad \textbf{D}\\ &\begin{aligned}\vec{u}+\vec{v}&=\begin{pmatrix} ^{2}\log 32\\ -\, ^{5}\log \displaystyle \frac{1}{625} \end{pmatrix}+\begin{pmatrix} -9\\ -21 \end{pmatrix}\\ &=\begin{pmatrix} 5-9\\ 4-21 \end{pmatrix}\\ &=\begin{pmatrix} -4\\ -17 \end{pmatrix} \end{aligned} \end{array}$

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