Does a scaled vector have the same orientation as the vector?

Yes — scaling changes the *length* of a vector, but
not its orientation.

In the diagram **w** and **v** are any two vectors.
We want a vector **u** that is orthogonal to **v**.
And we want scalar k so that:

w= kv+u

Then k**v** is called the **projection** of **w** onto **v**.

The vector **u** is orthogonal to **v**.
What is true of **u · v**?