[color=#134f5c][size=150]Imagine it's a clear day and the sun is shining down upon the Earth.[br][br]Let's pretend that the line containing [b]vector v[/b] is the ground. [br]Let's pretend that [b]vector u is a stick[/b] with one endpoint [b]on the ground[/b] and one endpoint in the air. [br][br]Since the sun is shining brightly, [b]vector u[/b] would therefore cast a shadow on the ground, no? [br][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][/size][/color]