Vector
A magnitude and a direction bundled into one object, written \langle x,y,z\rangle or \mathbf{v}.
A vector is a magnitude and a direction bundled into one object, written in component form as \langle x, y\rangle (or \langle x,y,z\rangle in space) or in bold as \mathbf{v}. A vector is fixed by its magnitude and direction alone, never by where its tail is drawn — two arrows with the same length and tilt are the same vector even if drawn starting from different points. The vector from P_1(x_1,y_1,z_1) to P_2(x_2,y_2,z_2) is \overrightarrow{P_1P_2}=\langle x_2-x_1,\,y_2-y_1,\,z_2-z_1\rangle.
Examples
The vector from (1,1,1) to (4,3,2) and the vector from (0,0,0) to (3,2,1) are the same vector \langle 3,2,1\rangle.
A drone's flight plan "go 40m east, 15m north, climb 8m" is a vector, regardless of where the drone launches from.