Answer
The horizontal component of $\mathbf{v}$ is a. The vertical component of $\mathbf{v}$ is b. The magnitude of $\mathbf{v}$ is given by $\left\| \mathbf{v} \right\|=\sqrt{{{a}^{2}}+{{b}^{2}}}$.
Work Step by Step
Consider the point V which has coordinates (a, b); this means the horizontal projection is a, and the vertical projection will be b; it can be represented in vector form $\mathbf{v}$ from (0, 0) to (a, b) as:
$\mathbf{v}=a\mathbf{i}+b\mathbf{j}$
Then vector $\mathbf{v}$ is called a position vector.
Hence, the horizontal component of $\mathbf{v}$ is a. The vertical component of $\mathbf{v}$ is b which has magnitude: $\sqrt{{{a}^{2}}+{{b}^{2}}}$
