(adsbygoogle = window.adsbygoogle || []).push({}); I hate Vector Algebra!!

I am having some trouble doing some vector algebra and any help or direction is greatly appreciated.

In our lecture we drew a vectorC(s)=A+ s(B-A)which described a line passing through pointsAandBand found that the vector of min. length (shortest dist. from origin to line) was given by s_{o}= [A (dot) (A-B)]/[|B-A|^{2}. The actual problem is to plug s_{o}into C(s) to show that C(s_{o}) = (sqrt(|A|^{2}|B|^{2}- (A dot B)^{2}))/(|B-A|).

What I have so far consists of changing [A (dot) (A-B)]/[|B-A|^{2}to [-A (dot) (B-A)]/[|B-A|^{2}so I can square the (B-A) however, when I do that I do not know how to then multiply that by the dot product of A. I know that A dot (B-A) is A dot B minus A dot A (A squared) but I have no idea how to do A dot (B-A)^{2}. Thanks for any help.

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# I hate Vector Algebra

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