Question: Can we represent the same vector, \(\vec{v}\), in a different way?
Answer: Yes, by using the notion of algebraic vectors.
To represent a geometric vector algebraically, position the tail of the vector, \(\vec{v}\), at the origin of a Cartesian \((x,y)\)-plane.
In our case, \(\lvert \vec{v}\rvert=10\) and the direction is north \(45^\circ\) east, which corresponds to an angle of \(45^\circ\) CCW (counter-clockwise) from the positive \(x\)-axis (this is defined as standard position).
We can now represent vector \(\vec{v}\) using coordinates \(x\) and \(y\), where \((x,y)\) is the location of the tip of vector \(\vec{v}\) when its tail is positioned at the origin.