Given any (nonzero) vectors [color=#000][math]\vec v[/math][/color] and [color=#000][math]\vec w[/math][/color], you can always split [color=#000][math]\vec v[/math][/color] into the sum of two vectors [color=#ff0000][math]\vec v_1[/math][/color] and [color=#0000ff][math]\vec v_2[/math][/color], with [color=#ff0000][math]\vec v_1[/math][/color] in the same direction as [color=#000][math]\vec w[/math][/color] and [color=#0000ff][math]\vec v_2[/math][/color] orthogonal to [color=#000][math]\vec w[/math][/color].[br][br]In the illustration below, you are free to drag the tips of the vectors [color=#000][math]\vec v[/math][/color] and [color=#000][math]\vec w[/math][/color].