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 kv is called the projection of w onto v.
The vector u is orthogonal to v. What is true of u · v?