Tentukan vektor satuan dari vektor - vektor berikut! Vektor adalah besaran yang memiliki nilai dan arah. Penulisannya bisa ditulis dalam 2 huruf kapital atau 1 huruf kecil. Penulisan vektor bisa dalam bentuk
Baris: u = (u₁, u₂)
Kolom: u =
Basis: u = u₁i + u₂j
Besar atau panjang vektor u:
|u| = √(u₁² + u₂²)
Vektor satuan adalah vektor yang panjangnya sama dengan satu
Verified answer
Tentukan vektor satuan dari vektor - vektor berikut! Vektor adalah besaran yang memiliki nilai dan arah. Penulisannya bisa ditulis dalam 2 huruf kapital atau 1 huruf kecil. Penulisan vektor bisa dalam bentuk
Besar atau panjang vektor u:
Vektor satuan adalah vektor yang panjangnya sama dengan satu
Vektor satuan u =
.u
Pembahasan
a) u =![\left[\begin{array}{cc}8\\6\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D8%5C%5C6%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{cc}8\\6\end{array}\right]")
|u| = √(8² + 6²)
|u| = √(64 + 36)
|u| = √(100)
|u| = 10
Jadi vektor satuan u adalah
=
.u
=![\frac{1}{10} . \left[\begin{array}{cc}8\\6\end{array}\right]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7D+.+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D8%5C%5C6%5Cend%7Barray%7D%5Cright%5D+ "\frac{1}{10} . \left[\begin{array}{cc}8\\6\end{array}\right]")
=![\left[\begin{array}{cc}\frac{8}{10}\\ \frac{6}{10} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B8%7D%7B10%7D%5C%5C+%5Cfrac%7B6%7D%7B10%7D+%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{cc}\frac{8}{10}\\ \frac{6}{10} \end{array}\right]")
=![\left[\begin{array}{cc}\frac{4}{5}\\ \frac{3}{5} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B4%7D%7B5%7D%5C%5C+%5Cfrac%7B3%7D%7B5%7D+%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{cc}\frac{4}{5}\\ \frac{3}{5} \end{array}\right]")
b) b =![\left[\begin{array}{cc}-5\\12\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-5%5C%5C12%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{cc}-5\\12\end{array}\right]")
|b| = √((-5)² + 12²)
|b| = √(25 + 144)
|b| = √(169)
|b| = 13
Jadi vektor satuan b adalah
=
.b
=![\frac{1}{13} . \left[\begin{array}{cc}-5\\12\end{array}\right]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B13%7D+.+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-5%5C%5C12%5Cend%7Barray%7D%5Cright%5D+ "\frac{1}{13} . \left[\begin{array}{cc}-5\\12\end{array}\right]")
=![\left[\begin{array}{cc}-\frac{5}{13}\\ \frac{12}{13} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-%5Cfrac%7B5%7D%7B13%7D%5C%5C+%5Cfrac%7B12%7D%7B13%7D+%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{cc}-\frac{5}{13}\\ \frac{12}{13} \end{array}\right]")
c) s =![\left[\begin{array}{ccc}3\\-2\\6\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C-2%5C%5C6%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}3\\-2\\6\end{array}\right]")
|s| = √(3² + (-2)² + 6²)
|s| = √(9 + 4 + 36)
|s| = √(49)
|s| = 7
Jadi vektor satuan s adalah
=
.s
=![\frac{1}{7} . \left[\begin{array}{ccc}3\\-2\\6\end{array}\right]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B7%7D+.+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C-2%5C%5C6%5Cend%7Barray%7D%5Cright%5D+ "\frac{1}{7} . \left[\begin{array}{ccc}3\\-2\\6\end{array}\right]")
=![\left[\begin{array}{cc}\frac{3}{7}\\ -\frac{2}{7} \\ \frac{6}{7} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B3%7D%7B7%7D%5C%5C+-%5Cfrac%7B2%7D%7B7%7D+%5C%5C+%5Cfrac%7B6%7D%7B7%7D+%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{cc}\frac{3}{7}\\ -\frac{2}{7} \\ \frac{6}{7} \end{array}\right]")
d) t =![\left[\begin{array}{ccc}12\\3\\4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D12%5C%5C3%5C%5C4%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}12\\3\\4\end{array}\right]")
|t| = √(12² + 3² + 4²)
|t| = √(144 + 9 + 16)
|t| = √(169)
|t| = 13
Jadi vektor satuan t adalah
=
.t
=![\frac{1}{13} . \left[\begin{array}{ccc}12\\3\\4\end{array}\right]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B13%7D+.+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D12%5C%5C3%5C%5C4%5Cend%7Barray%7D%5Cright%5D+ "\frac{1}{13} . \left[\begin{array}{ccc}12\\3\\4\end{array}\right]")
=![\left[\begin{array}{cc}\frac{12}{13}\\ \frac{3}{13} \\ \frac{4}{13} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B12%7D%7B13%7D%5C%5C+%5Cfrac%7B3%7D%7B13%7D+%5C%5C+%5Cfrac%7B4%7D%7B13%7D+%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{cc}\frac{12}{13}\\ \frac{3}{13} \\ \frac{4}{13} \end{array}\right]")
Pelajari lebih lanjut
Contoh soal lain tentang panjang vektor
brainly.co.id/tugas/14271227
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Detil Jawaban
Kelas : 10
Mapel : Matematika
Kategori : Vektor
Kode : 10.2.5
Kata Kunci : Tentukan vektor satuan dari vektor - vektor berikut!