# Vector Projections (1)

- Author:
- Tim Brzezinski

Imagine it's a clear day and the sun is shining down upon the Earth.
Let's pretend that the line containing

**vector v**is the ground. Let's pretend that**vector u is a stick**with one endpoint**on the ground**and one endpoint in the air. Since the sun is shining brightly,**vector u**would therefore cast a shadow on the ground, no?**The projection of u onto v is another vector**that is**parallel to v**and**has a length equal to what vector u's shadow would be (if it were cast onto the ground).**What condition(s) would cause the projection of u onto v to be equal to u itself?

What condition(s) wold cause the projection of u onto v to be equal to the zero vector <0,0>?