Greetings,

I would like to ask whether the cosine of the angle between two vectors can be derived from the knowledge of directional cosines. If that is the case, how can I prove the statement? I am attaching a scanned page from the book Vector and Tensor Analysisby Hay, which illustrates the concept beginning with the phrase, "By a formula from of analytic geometry..." and writes the formula, around which I have put a red box, below this statement. I have put a red rectangular box to emphasize my point.

Thanks