[color=#000000]Imagine it's a clear day and the sun is shining down upon the Earth.[br][br]Let's pretend that the line containing [/color][b][color=#cc0000]vector v[/color][/b][color=#000000] is the ground. [br][/color][color=#000000]Let's pretend that [/color][color=#0000ff][b]vector u is a stick[/b][/color][color=#000000] with one endpoint [/color][color=#cc0000][b]on the ground[/b][/color][color=#000000] and one endpoint in the air. [br][br]Since the sun is shining brightly, [/color][b][color=#0000ff]vector u[/color][/b][color=#000000] would therefore cast a shadow on the ground, no? [br][/color][color=#000000][b][br]The projection of u onto v is another vector[/b] that is [b]parallel to v[/b] and [b]has a length equal to what vector u's shadow would be (if it were cast onto the ground). [/b][/color]