||
Membaca
SMK Teknologi dan Rekayasa

Soal 51 Besar Sudut antara Dua Vektor


Vektor\ \bar{a}=-\bar{i}-3\bar{j}+2\bar{j}\ dan\ \bar{b}=3\bar{i}+2\bar{j}+\bar{k}.\\Besar\ sudut\ antara\ vektor\ \bar{a}\ dan\ \bar{b}\ adalah\ ....\\a.\ \ 120^{^{\circ}}\ \ \ \ \ \ \ \ \ \ b.\ \ 60^{^{\circ}}\ \ \ \ \ \ \ \ \ \ c.\ \ 45^{^{\circ}}\ \ \ \ \ \ \ \ \ \ d.\ \ 35^{^{\circ}}\ \ \ \ \ \ \ \ \ \ e.\ \ 30^{^{\circ}}
Jawaban: a

\bar{a}=-\bar{i}-3\tilde{j}+2\tilde{k}
\bar{b}=3\bar{i}+2\tilde{j}+\tilde{k}
\bar{a}.\bar{b}=-1.3+(-3).2+2.1=-3+(-6)+2=-7
\begin{vmatrix} \bar{a} \end{vmatrix}=\sqrt{(-1)^{2}+(-3)^{2}+2^{2}}=\sqrt{1+9+4}=\sqrt{14}
\begin{vmatrix} \bar{b} \end{vmatrix}=\sqrt{3^{2}+2^{2}+1^{2}}=\sqrt{9+4+1}=\sqrt{14}
Misalkan\ \alpha \ adalah\ besar\ sudut\ yang\ dibentuk\ vektor\ \bar{a}\ dan\ \bar{b},\ maka:
\begin{array}{rcl}cos\ \alpha &=&\frac{\bar{a}.\bar{b}}{\begin{vmatrix} \bar{a} \end{vmatrix}.\begin{vmatrix} \bar{b} \end{vmatrix}}\\\\&=&\frac{-7}{\sqrt{14}.\sqrt{14}}\\\\&=&\frac{-7}{14}\\\\&=&-\frac{1}{2}\end{array}
Karena\ nilai\ cos\ \alpha \ negatif,\ maka\ \alpha \ adalah\ sudut\ tumpul\\(sudut\ di\ kuadran\ II),\ sehingga\ \alpha =(180-60)^{^{\circ}}=120^{^{\circ}}.

About Kalakay

Guru Matematika SMK

Diskusi

One thought on “Soal 51 Besar Sudut antara Dua Vektor

  1. bagaimana cara mengubah 1/2 ke dalam derajat ? Caranya ?

    mohon bantuannya🙂

    Posted by jodi | 5 Maret 2013, 5:02 PM

Tinggalkan Balasan

Isikan data di bawah atau klik salah satu ikon untuk log in:

Logo WordPress.com

You are commenting using your WordPress.com account. Logout / Ubah )

Gambar Twitter

You are commenting using your Twitter account. Logout / Ubah )

Foto Facebook

You are commenting using your Facebook account. Logout / Ubah )

Foto Google+

You are commenting using your Google+ account. Logout / Ubah )

Connecting to %s

%d blogger menyukai ini: