panjang vektor →ab=ab→= 4,6 Satuan Panjang
Penjelasan dengan langkah-langkah:
Diketahui :
Titik P (2,1,1) dan titik Q (5,7,1), membagi ruas garis PQ
→PA:→AQ =1:4
Sedangkan titik b (6,3,4), tentukan →AB
Sebelumnya kita harus mencari dulu nilai A, misal (x,y,z)
→PA = A - P →AQ = Q - A
= [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] \\[/tex]-[tex]\left[\begin{array}{ccc}2\\1\\1\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}x-2\\y-1\\z-1\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}5\\7\\1\end{array}\right][/tex]-[tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}x-5\\y-7\\z-1\end{array}\right][/tex]
Karena →PA : →AQ = 1 : 4
→PA = [tex]\frac{1}{4}[/tex]
4→PA = → AQ
4 [tex]\left[\begin{array}{ccc}x-2\\y-1\\z-1\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}5-x\\7-y\\1-z\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}4x-8\\4y-4\\4z-4\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}5-x\\7-y\\1-z\end{array}\right][/tex]
sehingga -4x-8 = 5-x -4y-4 = 7 - y 4z - 4 = 1 - z
4x+x = 5 + 8 4y + y = 7 + 4 4z + z = 1 + 4
5x = 13 5y = 11 5z = 5
x = [tex]\frac{13}{5}[/tex] y = 11/5 z = 1
maka A [tex]\left[\begin{array}{ccc}b/5\\11/5\\1\end{array}\right][/tex] maka →AB = [tex]\sqrt{\left \ 17/5\\} ^{2} + \left {{4/5} . ^{2} + 3^{2[/tex]
= [tex]\sqrt{289/25 + 16/25 + 9}[/tex]
= [tex]\sqrt{289/25+16/25+225/25}[/tex]
= [tex]\sqrt{530/25}[/tex] = [tex]\sqrt{106/25}[/tex]
= 4,6
Kesimpulan :
jika titik a membagi ruas garis pq dengan perbandingan →pa:→aq=1:4.pa→:aq→=1:4. jika koordinat titik b(6,3,4), panjang vektor →ab=ab→= 4,6
Pelajari Lebih Lanjut :
Pelajari lebih lanjut materi tentang Garis Singgung pada https://brainly.co.id/tugas/26987792
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