Using a [i][b]unit vector[/b][/i], that is a vector whose length is 1, we can write any vector [math]\vec{v}[/math] as [math]\vec{v}=v\hat{u}_v[/math], where [math]v[/math] is the length of [math]\vec{v}[/math] and [math]\hat{u}_v[/math] is the unit vector that defines the direction of [math]\vec{v}[/math].[br][br][br]
We can extend in a natural way the description of the position of any point using Cartesian coordinates to vectors. [br]By associating with the [i]x[/i]-axis its unit vector [math]\hat{i}[/math] and with the [i]y[/i]-axis its unit vector [math]\hat{j}[/math], we can write any vector as the combination of its oriented components using the [b][i]Cartesian notation[/i][/b]: [br][math]\vec{v}=\vec{v_x}+\vec{v_y}=v_x\hat{i}+v_y\hat{j}[/math].
Write the following vectors in Cartesian notation:[br]- The tail of [math]\vec{v}[/math] is at the origin, and the tip is at the point [math]\left(-3,-2\right)[/math].[br]- The tail of [math]\vec{w}[/math] is at [math]\left(2,2\right)[/math] and the tip is at [math]\left(5,-6\right)[/math].[br]- [math]\vec{u}[/math] is the opposite of [math]\vec{v}[/math].