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The 5.8 crux pitch features an...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/1664350/34a08e8cf2755ed4884b87c1416d7425/564x318_1"},"target":"_self","position":"0","reqid":"1769570512324472-14047125204995649760-balancer-l7leveler-kubr-yp-sas-18-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D65cuSCJWL64","linkTemplate":"/video/preview/1792157358203037736?parent-reqid=1769570512324472-14047125204995649760-balancer-l7leveler-kubr-yp-sas-18-BAL&text=Calculus+Climber&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Climbing 'Calculus Crack' in Squamish","related_orig_text":"Calculus Climber","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Calculus Climber\",\"url\":\"http:\\/\\/www.youtube.com\\/watch?v=65cuSCJWL64\",\"src\":\"serp\",\"rvb\":\"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-AaCBCQBgAQrKosBEAEaeIH9B_4N_gIA-_z_DwEJ-wIEAAAC-P_-APj9_gMFAv8ABQH6AfcBAAAFDgP3CQAAAPj5-w___wAAFf0M9gQAAAAQ-vUB9QAAAAb4-P4LAAEBCwvzCwP_AAAR-AsMAAAAAPkO-xD_AAAA9voK_wAAAAAB8AcOAAAAACAALY2P2js4E0AJSE5QAipzEAAaYDUpABgp8fACvT3iAjMNNe0gp_uWuBj_Qvj_8yfvHgYZybobIgDVygvgoAAAAA6_7l8BANp_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_AACAwgAAMEEgADgTQAlIdVABKo8CEAAagAIAAAS-AABQPQAAqD0AAKC8AAB0PgAAUD0AAIA7AAAJvwAATL4AAMg9AABwvQAAmL0AABw-AADYPQAAJL4AAMi9AAAEPgAABD4AAOC8AAC6PgAAfz8AADS-AABEvgAALD4AAKC8AAA8vgAAQDwAAOA8AABcPgAAhj4AAEA8AACevgAAir4AACQ-AABQPQAA6L0AAIA7AADGvgAAmr4AAKq-AADgvAAALD4AAEw-AABAvAAAPL4AANi9AACgvAAATD4AANg9AAAUvgAAQLwAAEQ-AAAkPgAAij4AAGS-AACAuwAALz8AADw-AABEPgAAmD0AAGS-AABAvAAA4DwAADS-IAA4E0AJSHxQASqPAhABGoACAACOvgAAPD4AAKC8AABDvwAAQDwAAAy-AAAwPQAABL4AAFC9AACgPAAADD4AACS-AACgvAAA6L0AADA9AAC4vQAAqL0AAO4-AADIvQAATD4AAJo-AADoPQAA6D0AABy-AACgPAAAXL4AAHS-AAAEPgAA6D0AAFC9AAAMPgAADD4AABy-AACIvQAAiD0AAAy-AABMPgAAjj4AAGS-AAD4vQAAHD4AALi9AAC4vQAA4LwAAMg9AADgPAAAf78AAK4-AABMPgAARD4AANg9AACgPAAAUD0AALY-AAAcvgAADD4AAIi9AACgPAAAMD0AAAy-AACIvQAABL4AAIo-AABQPSAAOBNACUh8UAEwCTgBSgBgAGgA\"}","related_url":"http://www.youtube.com/watch?v=65cuSCJWL64","parent-reqid":"1769570512324472-14047125204995649760-balancer-l7leveler-kubr-yp-sas-18-BAL","related_vfp":1,"relatedVideo":"yes"},"cwidth":1280,"cheight":720,"cratio":1.77777,"dups":["1792157358203037736"],"episode":0,"season":0,"isEmbedOnly":false,"greenHost":"YouTube","hasTranslation":true,"contentTypeId":null,"censored":false},"5507845520427221817":{"videoId":"5507845520427221817","docid":"34-7-3-ZB3395B397A893125","description":"BUders üniversite matematiği derslerinden calculus-I dersine ait \"Uzayda Doğru Denklemini Yazma\" videosudur. Hazırlayan: Kemal Duran (Matematik Öğretmeni) http://www.buders.com/kadromuz.html...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2968351/d78706d1d3b142eecdeb98d896edc06c/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/teRrBgEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"1","reqid":"1769570512324472-14047125204995649760-balancer-l7leveler-kubr-yp-sas-18-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769570512324472-14047125204995649760-balancer-l7leveler-kubr-yp-sas-18-BAL&text=videoid:5507845520427221817","teaser":[{"list":{"type":"unordered","items":["Bu video, matematik eğitimi formatında uzayda doğru denklemlerinin nasıl yazılacağını anlatan bir ders anlatımıdır.","Video, uzayda doğru denklemini yazmak için gerekli iki bilginin (doğrunun üzerinde bir nokta ve doğruya paralel bir vektör) açıklamasıyla başlar. Ardından uzayda doğru denkleminin iki farklı yazım şekli (kapalı denklem ve parametrik denklem) detaylı olarak anlatılır. Video, teorik bilgilerin ardından üç farklı örnek üzerinden konuyu pekiştirir. Örnekler arasında doğrunun üzerindeki nokta ve paralel vektör verilen durumlar, vektörde sıfır koordinatı bulunan durumlar ve doğrunun üzerinde iki nokta verilen durumlar ele alınır."]},"endTime":820,"title":"Uzayda Doğru Denklemleri Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Uzayda Doğru Denkleminin Yazımı","list":{"type":"unordered","items":["Uzayda doğru denklemini yazabilmek için iki bilgiye ihtiyaç vardır: doğrunun üzerinde bir nokta ve doğruya paralel bir vektör.","Doğrunun üzerindeki nokta (x, y, z) ve paralel vektör (a, b, c) bilgileriyle doğru denklemi yazılabilir.","Uzayda doğru denklemi, (x-x₀)/a = (y-y₀)/b = (z-z₀)/c şeklinde yazılır."]},"beginTime":1,"endTime":175,"href":"/video/preview/5507845520427221817?parent-reqid=1769570512324472-14047125204995649760-balancer-l7leveler-kubr-yp-sas-18-BAL&text=Calculus+Climber&t=1&ask_summarization=1"},{"index":1,"title":"Parametrik Doğru Denklemi","list":{"type":"unordered","items":["Uzayda doğru denkleminin başka bir yazım şekli parametrik denklemidir.","Parametrik denklemde x = a + at, y = b + bt, z = c + ct şeklinde yazılır.","Parametrik denklemde t parametresi kullanılır ve doğrunun her noktasını belirler."]},"beginTime":175,"endTime":238,"href":"/video/preview/5507845520427221817?parent-reqid=1769570512324472-14047125204995649760-balancer-l7leveler-kubr-yp-sas-18-BAL&text=Calculus+Climber&t=175&ask_summarization=1"},{"index":2,"title":"Örneklerle Doğru Denkleminin Yazılması","list":{"type":"unordered","items":["(-1, 2, 3) noktasından geçen ve (2, 1, 5) vektörüne paralel olan doğrunun denklemi (x+1)/2 = (y-2)/1 = (z-3)/5 şeklinde yazılır.","Parametrik denklemi ise x = 2t - 1, y = t + 2, z = 5t + 3 olarak bulunur.","Doğrunun kapalı denkleminde paydalar paralel vektörü, paylar ise doğru üzerindeki noktayı verir."]},"beginTime":238,"endTime":446,"href":"/video/preview/5507845520427221817?parent-reqid=1769570512324472-14047125204995649760-balancer-l7leveler-kubr-yp-sas-18-BAL&text=Calculus+Climber&t=238&ask_summarization=1"},{"index":3,"title":"Sıfır Koordinatlı Vektörlerde Doğru Denklemi","list":{"type":"unordered","items":["(1, 2, 5) noktasından geçen ve (3, 0, 5) vektörüne paralel olan doğrunun denklemi (x-1)/3 = z-5/5, y=2 şeklinde yazılır.","Parametrik denklemi ise x = 3t + 1, y = 2, z = 5t + 5 olarak bulunur.","Vektörde sıfır koordinatı olduğunda, o koordinatın yerine denklemde y=2 gibi bir denklem yazılır."]},"beginTime":446,"endTime":608,"href":"/video/preview/5507845520427221817?parent-reqid=1769570512324472-14047125204995649760-balancer-l7leveler-kubr-yp-sas-18-BAL&text=Calculus+Climber&t=446&ask_summarization=1"},{"index":4,"title":"İki Noktadan Geçen Doğrunun Denklemi","list":{"type":"unordered","items":["İki noktadan geçen doğrunun denklemini yazmak için önce paralel vektörü 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Ardından verilen örnek soruyu çözer: S(2, -3, 4) noktasının x + 2y + 2z - 13 düzlemine olan uzaklığını hesaplar. Sonuç olarak, noktanın düzleme olan uzaklığının 3 birim olduğunu bulur."]},"endTime":137,"title":"Uzay Geometri Örnek Soru Çözümü","beginTime":0}],"fullResult":[{"index":0,"title":"Uzay Geometrisi Örnek Soru","list":{"type":"unordered","items":["Video, uzay geometri konusuna bir örnek sorunun çözümünü sunuyor.","Soru: S(2, -3, 4) noktasının x + 2y + 2z = 13 düzlemine olan uzaklığı bulunuyor."]},"beginTime":0,"endTime":18,"href":"/video/preview/10997095666253666821?parent-reqid=1769570512324472-14047125204995649760-balancer-l7leveler-kubr-yp-sas-18-BAL&text=Calculus+Climber&t=0&ask_summarization=1"},{"index":1,"title":"Noktanın Düzleme Uzaklığı Formülü","list":{"type":"unordered","items":["Bir noktanın bir düzlemi uzaklığı, en kısa olan dik uzaklıktır.","Formül: d = |ax₁ + by₁ + cz₁ + d| / √(a² + b² + c²)","Formülde || işaretinin amacı uzaklığın negatif çıkmamasıdır."]},"beginTime":18,"endTime":73,"href":"/video/preview/10997095666253666821?parent-reqid=1769570512324472-14047125204995649760-balancer-l7leveler-kubr-yp-sas-18-BAL&text=Calculus+Climber&t=18&ask_summarization=1"},{"index":2,"title":"Örnek Sorunun Çözümü","list":{"type":"unordered","items":["Formülde x = 2, y = -3, z = 4 değerleri yerine konulur.","Hesaplamalar: 2 + (-3) × 2 + 4 × 2 - 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