vektorski umnožak - Hrvatska enciklopedija

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preslikavanje koje zadovoljava sljedeća svojstva:1. a × b = 0 ako je a = 0 ili b = 0 ili ako su vektori a i b kolinearni2. a × b = −b × a (antikomutativnost)3. a × (b + c) = a × b + a × c (distributivnost)4. λ (a × b) = (λa) × b = a × (λb) (homogenost).Vektorski umno&scaron;ci <a href="https://www.enciklopedija.hr/clanak/jedinicni-vektor">jediničnih vektora</a> i, j, k (u pravokutnome Kartezijevu koordinatnom sustavu vektori u smjerovima osi x, y i z) imaju sljedeća svojstva:1. i × i = j × j = k × k = 02. i × j = k, j × k = i, k × i = j3. j × i = –k, k × j = –i, i × k = –j.Vektorski umnožak<a href="https://www.enciklopedija.hr/clanak/radijvektor"> radijvektora</a> a = axi + ayj + azk i radijvektora b = bxi + byj + bzk jest:a × b = (aybz – azby) i + (azbx – axbz) j + (axby – aybx) k ili<img style="vertical-align:middle" src="https://media.lzmk.hr/he/wmf/vektorski produkt.jpg" alt="vektorski produkt.jpg"/>.Za dvostruki vektorski umnožak vrijedi: (a × b) × c = (a · c) b – (b · c) a. </div> </div> </div> <div class="container citiranje"> Citiranje: vektorski umnožak. Hrvatska enciklopedija, mrežno izdanje. Leksikografski zavod Miroslav Krleža, 2013. – 2024. Pristupljeno 25.11.2024. <https://www.enciklopedija.hr/clanak/vektorski-umnozak>. </div> <div class="container d-print-none"></div> <div class="container d-print-none"> <button type="button" class="btn btn-secondary" data-bs-toggle="modal" data-bs-target="#mkomentar">Komentar</button> </div> <div class="modal fade" tabindex="-1" id="mkomentar"> <div class="modal-dialog modal-dialog-centered"> <div class="modal-content"> <div class="modal-header"> <h5 class="modal-title">Unesite komentar</h5> <button type="button" class="btn-close" data-bs-dismiss="modal" aria-label="Close"></button> </div> <div class="modal-body"> Komentar: <textarea style="width:100%; height:300px" id="taKomentar" name="taKomentar"></textarea> Potpis: <input type="text" style="width:100%" id="taPotpis" name="taPotpis" /input> </div> <div class="modal-footer"> <button type="button" class="btn btn-secondary" data-bs-dismiss="modal">Zatvori</button> <button type="submit" class="btn btn-primary" title="Snimi" value="Snimi" formaction="/Clanak/vektorski-umnozak?handler=ButtonSnimi">Pošalji</button> </div> </div> </div> </div> <input name="__RequestVerificationToken" type="hidden" value="CfDJ8AafmPaswmdEooPiIBQpxHBs357KNWHmCjsql31lVWUVOnpAY9cPj59sgw-CrSB1-kXNGwkxXSaGEkYcRojZ8rHN9T-dAkGmeMfS8ZMBDuSi-hcrnOmx7JmZdMmSZKFEsQsCoqxD4X6vyjoYSnBwbdc" /></form> <script src="/lib/lightbox2/js/lightbox.min.js"></script> <script> lightbox.option({ 'resizeDuration': 200, 'wrapAround': false, 'albumLabel': "slika %1 od %2" }) </script> </main> </div> <div b-5bzbccjy93> <div id="cookieConsent" class="alert alert-info alert-dismissible fade show fixed-bottom" role="alert"> <div class="container"> Naše web stranice koriste kolačiće kako bi Vam omogućili najbolje korisničko iskustvo, za analizu prometa i korištenje društvenih mreža. <a href="/UvjetiKoristenja">Doznaj više.</a> </div> <div class="d-grid gap-2 d-md-flex justify-content-md-end"> <button type="button" class="btn btn-secondary accept-policy me-md-2" data-dismiss="alert" aria-label="Close" data-cookie-string=".AspNet.Consent=yes; expires=Tue, 25 Nov 2025 03:41:30 GMT; path=/; secure; samesite=none">Prihvati</button> </div> </div> <script> (function () { var button = document.querySelector("#cookieConsent button[data-cookie-string]"); button.addEventListener("click", function (event) { document.cookie = button.dataset.cookieString; $("#cookieConsent").hide(); }, false); })(); </script> </div> <footer b-5bzbccjy93 class="border-top footer text-muted" id="myFooter"> <div b-5bzbccjy93 class="container text-center"> <img style="height:48px; vertical-align:text-top;" src="/images/lzmklogo.png" /> </div> <div b-5bzbccjy93 class="container text-center"> © 2024. <a b-5bzbccjy93 href="https://www.lzmk.hr">Leksikografski zavod Miroslav Krleža</a> </div> </footer> <button b-5bzbccjy93 type="button" title="Top" class="btn btn-secondary btn-floating btn-lg" id="btn-back-to-top"> <svg b-5bzbccjy93 xmlns="http://www.w3.org/2000/svg" width="18" height="18" fill="currentColor" class="bi bi-caret-up-fill"> <path b-5bzbccjy93 d="m7.247 4.86-4.796 5.481c-.566.647-.106 1.659.753 1.659h9.592a1 1 0 0 0 .753-1.659l-4.796-5.48a1 1 0 0 0-1.506 0z" /> </svg> </button> <script src="/lib/bootstrap/dist/js/bootstrap.bundle.min.js"></script> <script src="/js/site.js?v=HFdDLbM0HxvrAwFgkX5IgRBv1htKZvv7gXFyyLjyFbI"></script> </body> </html>

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vektorski umnožak - Hrvatska enciklopedija