Relating dot product divided with square of the vector while changing basis of vector

  • I'm fairly sure that the question is very easy, but I find it unlikely that anyone is going through the video for the current bounty. I think you should either increase it, or try to write your question clearly without referencing external sources.

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  • Your post was kind of vague but I decided to answer as I thought this might be the first time you are asking a question here. Please make sure to be much more clear about your questions in future, otherwise you may not get a response.

  • Thanks for the helpful answer. Is it true that the distance marked P in the diagram equal in magnitude? Also, it will help if you are kind enough to confirm the length of P starts from where a1 ends. If that be so, then I find some meaning breaking OM into Oa1 and a1M. That is, a1M = MN = P.

  • Root 5 I understand is length of Oa1 and not ON.

  • From another thread, the magnitude of MN appears 1 (https://mathforums.com/threads/relating-dot-product-divided-with-square-of-the-vector-while-changing-basis-of-vector.362851/#post-665818). An insight will help why I am confused.

  • Regarding your first comment: Yes, the distance marked P in the diagram equal in magnitude of the Vector MN. Yes, I confirm.

  • Regarding your second comment: Sorry, I do not answer questions in other platforms.

The answer is accepted.