Question

What are components of a vector?

Answer 1

If a vector $\mathbf{v}$ in 2 -space or 3 -space is positioned with its initial point at the origin of a rectangular coordinate system, then the vector is completely determined by the coordinates of its terminal point. We call these coordinates the components of $\mathbf{v}$ relative to the coordinate system. We will write $\mathbf{v}=\left(v_{1}, v_{2}\right)$ to denote a vector $\mathbf{v}$ in 2-space with components $\left(v_{1}, v_{2}\right)$, and $\mathbf{v}=\left(v_{1}, v_{2}, v_{3}\right)$ to denote a vector $\mathbf{v}$ in 3 -space with components $\left(v_{1}, v_{2}, v_{3}\right)$.