Pengertian
Panjang vektor adalah panjang dari titik awal vektor sampai ke titik akhir vektor.
Rumus
- Vektor 2 dimensi
\[\vec{a} = \sqrt{x^2 + y^2}\]
\[\vec{AB} = \sqrt{(x_2-x_1)^2 + (y_2 -y_1)^2}\]
- Vektor 3 dimensi
\[\vec{d} = (x,y,z) = |\vec{d}| = \sqrt{x^2 + y^2 + z^2}\]
\[\vec{c} = (x_1,y_1,z_1), \vec{d} = (x_2, y_2, z_2) = |\vec{CD}| = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2 + (z_2 – z_1)}\]
Contoh
\[\vec{a} = (5,3), \vec{b} = (2,1)\]
\[Tentukan \ panjang \ vektor \vec{AB}!\]
\[\vec{AB} = \sqrt{(x_2-x_1)^2 + (y_2 -y_1)^2}\]
\[\vec{AB} = \sqrt{(2-5)^2 + (1 -3)^2}\]
\[\vec{AB} = \sqrt{9 +4}\]
\[\vec{AB} = \sqrt{13}\]