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


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

Projection of one Vector onto Another

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?