Vectors are represented by arrows indicating magnitude (length) and direction. Equivalent vectors have the same magnitude and direction regardless of starting point. Mathematically, vectors are denoted by lowercase bold letters (e.g., **a**) or with arrows (e.g., →a). In two dimensions, a vector is represented by an ordered pair (x, y), where x and y are the horizontal and vertical components respectively. The magnitude is calculated using the Pythagorean theorem. The concept extends to higher dimensions, though visualization becomes challenging beyond three. now, what's interesting about vectors is that we only care about the magnitude in the direction. we don't necessarily not care where we start, where we place it when we think about it visually like this and so we'll put our horizontal dimension first. so you might call this vector 5, 0. it's moving 5, positive 5 in the horizontal direction. and it's not moving at all in the vertical direction. and the notation might change. you might also see notation, and actually in the linear algebra context, it's more typical to write it as a column vector like this--5, 0. so this vector might be specified as 3, 4