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→A.→B  এবং C→ ভেক্টর তিনটি একই তলে হওয়ার শর্ত কোনটি ?

Created: 3 years ago | Updated: 3 months ago
Updated: 3 months ago
বাংলাদেশ কৃষি বিশ্ববিদ্যালয় শিক্ষাবর্ষঃ ২০১৬-২০১৭ পদার্থবিদ্যা ভেক্টর
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Best Ans:

ভেক্টরটি আয়তন নির্দেশ করে। ভেক্টরগুলো একই সমতলে থাকলে তাদের আয়তন শূন্য হয় বা থাকতে পারে না।

2 years ago
SHuvo Baidya

পদার্থবিদ্যা

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নিচের কোন সূত্রটা ভেক্টর বিভাজনে ব্যবহার করা হয়?

  j ও k  আয়ত একক ভেক্টরদ্বয় যে তলে অবস্থিত সেই তলের উপর লম্ব একক ভেক্টর হলো-

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F→=2i^+3j^-4k ^ বলটির ZX সমতলে মান কত?

6 N ওজনের একটি বস্তুকে 6 N বল দ্বারা চিত্রানুযায়ী টানা হচ্ছে। বস্তুটির আপাত ওজন- 
Promotion
MessagesTimelineExceptionsViews33RouteQueries29Models35Livewire0MailsGateSessionRequest
Request history8.2.27PHP Version139msRequest Duration35MBMemory UsageGET admission/single-questionRoute
    • Booting (87.34ms)time
    • Application (51.83ms)time
    • 1 x Booting (62.76%)
      87.34ms
      1 x Application (37.24%)
      51.83ms
      33 templates were rendered
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      • common.script.promotion_functionspromotion_functions.blade.php#?blade
      uri
      GET admission/single-question
      middleware
      web, throttle:global
      controller
      App\Http\Controllers\Academy\QuestionController@singleMcq
      namespace
      prefix
      where
      as
      admission.single-question
      file
      app/Http/Controllers/Academy/QuestionController.php:62-98
      29 statements were executed6.96ms
      • QuestionController.php#150debugerror_satt220μsselect `id`, `view_count`, `main_category_id` from `questions` where `questions`.`id` = '83767' and `questions`.`deleted_at` is null limit 1
        Bindings
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:150
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Http/Controllers/Academy/QuestionController.php:145
        • app/Http/Controllers/Academy/QuestionController.php:66
      • QuestionController.php#190debugerror_satt530μsupdate `questions` set `view_count` = `view_count` + 1 where `id` = 83767
        Bindings
        • 0: 83767
        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:190
        • vendor/laravel/framework/src/Illuminate/Cache/Lock.php:95
        • app/Http/Controllers/Academy/QuestionController.php:187
        • app/Http/Controllers/Academy/QuestionController.php:79
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      • QuestionController.php#256debugerror_satt200μsselect `id`, `view_count`, `vote`, `subject_id`, `category_id`, `sub_category_id`, `board_exam_id`, `passage_id`, `question_type`, `question`, `is_duplicate`, `status`, `image`, `meta_og_image`, `meta_og_title`, `meta_keyword`, `created_at`, `updated_at`, exists(select * from `review_contents` where `questions`.`id` = `review_contents`.`reviewable_id` and `review_contents`.`reviewable_type` = 'App\\Models\\Question') as `review_content_exists` from `questions` where `id` = '83767' and `questions`.`deleted_at` is null limit 1
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:256
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:256
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Http/Controllers/Academy/QuestionController.php:208
        • app/Http/Controllers/Academy/QuestionController.php:82
      • QuestionController.php#256debugerror_satt120μsselect `id`, `title`, `passage` from `passages` where `passages`.`id` in (0) and `passages`.`deleted_at` is null
        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:256
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Http/Controllers/Academy/QuestionController.php:208
        • app/Http/Controllers/Academy/QuestionController.php:82
      • QuestionController.php#256debugerror_satt120μsselect `id`, `name`, `slug`, `meta_og_image` from `sub_categories` where `sub_categories`.`id` in (4499) and `sub_categories`.`deleted_at` is null
        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:256
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Http/Controllers/Academy/QuestionController.php:208
        • app/Http/Controllers/Academy/QuestionController.php:82
      • QuestionController.php#256debugerror_satt140μsselect `id`, `name`, `des_updated_by`, `des_added_by`, `link_subject_id`, `slug` from `subjects` where `subjects`.`id` in (75) and `subjects`.`deleted_at` is null
        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:256
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Http/Controllers/Academy/QuestionController.php:208
        • app/Http/Controllers/Academy/QuestionController.php:82
      • QuestionController.php#256debugerror_satt190μsselect `id`, `description`, `subject_id` from `subject_descriptions` where `subject_descriptions`.`subject_id` in (75) and `subject_descriptions`.`deleted_at` is null
        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:256
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Http/Controllers/Academy/QuestionController.php:208
        • app/Http/Controllers/Academy/QuestionController.php:82
      • QuestionController.php#256debugerror_satt210μsselect `subjects`.`id`, `subjects`.`name`, `subjects`.`slug`, `subjectables`.`subjectable_id` as `pivot_subjectable_id`, `subjectables`.`subject_id` as `pivot_subject_id`, `subjectables`.`subjectable_type` as `pivot_subjectable_type`, `subjectables`.`created_user_id` as `pivot_created_user_id`, `subjectables`.`deleted_at` as `pivot_deleted_at`, `subjectables`.`status` as `pivot_status`, `subjectables`.`created_at` as `pivot_created_at`, `subjectables`.`updated_at` as `pivot_updated_at` from `subjects` inner join `subjectables` on `subjects`.`id` = `subjectables`.`subject_id` where `subjectables`.`subjectable_id` in (83767) and `subjectables`.`subjectable_type` = 'App\\Models\\Question' and `subjects`.`deleted_at` is null
        Bindings
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:256
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Http/Controllers/Academy/QuestionController.php:208
        • app/Http/Controllers/Academy/QuestionController.php:82
      • QuestionController.php#256debugerror_satt280μsselect * from `vote_statistics` where `vote_statistics`.`question_id` in (83767)
        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:256
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Http/Controllers/Academy/QuestionController.php:208
        • app/Http/Controllers/Academy/QuestionController.php:82
      • QuestionController.php#256debugerror_satt230μsselect * from `descriptions` where `descriptions`.`descriptionable_id` in (83767) and `descriptions`.`descriptionable_type` = 'App\\Models\\Question' and `status` in ('approve', 'active') and `descriptions`.`deleted_at` is null order by `vote` desc
        Bindings
        • 0: App\Models\Question
        • 1: approve
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:256
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Http/Controllers/Academy/QuestionController.php:208
        • app/Http/Controllers/Academy/QuestionController.php:82
      • QuestionController.php#256debugerror_satt140μsselect `id`, `name`, `avatar` from `users` where `users`.`id` in (42447) and `users`.`deleted_at` is null
        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:256
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Http/Controllers/Academy/QuestionController.php:208
        • app/Http/Controllers/Academy/QuestionController.php:82
      • QuestionController.php#256debugerror_satt150μsselect `id`, `bookmarkable_id`, `bookmarkable_type`, `user_id` from `bookmarks` where `bookmarks`.`bookmarkable_id` in (83767) and `bookmarks`.`bookmarkable_type` = 'App\\Models\\Question' and `user_id` is null
        Bindings
        • 0: App\Models\Question
        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:256
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Http/Controllers/Academy/QuestionController.php:208
        • app/Http/Controllers/Academy/QuestionController.php:82
      • QuestionController.php#256debugerror_satt170μsselect `id`, `votable_id`, `votable_type`, `user_id` from `votes` where `votes`.`votable_id` in (83767) and `votes`.`votable_type` = 'App\\Models\\Question' and `user_id` is null
        Bindings
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:256
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Http/Controllers/Academy/QuestionController.php:208
        • app/Http/Controllers/Academy/QuestionController.php:82
      • QuestionController.php#256debugerror_satt100μsselect `id`, `question_id`, `user_id`, `choosen_option` from `vote_logs` where `vote_logs`.`question_id` in (83767) and `user_id` is null
        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:256
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Http/Controllers/Academy/QuestionController.php:208
        • app/Http/Controllers/Academy/QuestionController.php:82
      • DynamicPrintService.php#99debugerror_satt560μsselect `subjectable_id` from `subjectables` where `subjectable_type` = 'App\\Models\\Question' and `subject_id` in (2235)
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        Backtrace
        • app/Services/DynamicPrintService.php:99
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Services/DynamicPrintService.php:96
        • app/Http/Controllers/Academy/QuestionController.php:409
      • QuestionController.php#451debugerror_satt1.2msselect `id`, `view_count`, `vote`, `subject_id`, `category_id`, `sub_category_id`, `board_exam_id`, `passage_id`, `question_type`, `question`, `is_duplicate`, `status`, `image`, `created_at`, `updated_at` from `questions` where `id` in (110355, 110703, 110817, 110825, 110902, 111198, 120594, 120761, 121711, 121720, 121810, 121903, 126831, 128886, 128896, 129212, 129897, 130821, 130866, 130879, 130968, 131221, 131333, 132613, 132973, 133337, 133349, 133492, 133963, 134539, 134559, 142143, 142145, 142147, 142571, 142573, 142680, 142870, 142872, 142957, 143005, 143021, 143062, 143181, 143532, 143586, 143730, 143835, 143846, 144027, 144126, 144173, 144185, 83767, 83977, 84117, 84273, 84353, 84385, 84854, 84951, 85225, 85444, 85445, 85467, 87216, 87230, 89522, 89796, 93946, 97767, 97876, 97981, 97993, 98061, 98085, 98166, 100162, 102029, 109578, 110083, 110189, 83777, 83790, 95033, 95142, 95388, 95428, 95449, 96085, 99162, 99173, 99337, 99601, 99662, 99753, 122562, 123642, 124343, 124808, 180297, 180455, 180714, 180903, 180993, 180994, 181072, 181089, 181147, 181204, 181239, 181298, 181390, 181395, 181576, 181577, 181724, 181737, 182126, 184694, 184705, 184773, 184831, 184832, 184968, 185160, 185165, 185243, 185244, 191564, 191645, 191660, 191704, 191897, 191985, 192181, 192237, 192726, 199433, 199497, 199572, 199730, 200103, 200150, 200330, 200420, 201482, 201876, 202674, 202791, 203979, 204206, 204583, 212353, 212406, 213233, 213564, 213574, 213667, 213680, 213725, 213819, 213865, 213913, 232850, 232938, 233174, 233254, 235249, 236833, 240611, 240941, 241125, 241288, 241785, 241788, 241850, 241953, 241964, 242672, 244420, 180671, 99551, 102737, 327276, 327297, 428923, 428924, 428925, 428926, 428927, 428928, 428929, 428930, 428931, 428932, 428933, 428934, 428935, 428936, 428937, 428938, 428939, 428940, 428941, 428942, 428943, 428944, 428945, 428946, 428947, 428948, 428949, 428950, 428951, 428952, 428953, 428954, 428955, 428956, 428957, 428958, 428959, 428960, 428961, 428962, 429038, 429039, 429040, 429041, 429042, 429043, 429044, 429045, 429046, 429047, 429048, 429049, 429050, 429051, 429052, 429053, 429054, 429055, 429056, 429057) and `id` != 83767 and `questions`.`deleted_at` is null order by `created_at` desc limit 6
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:451
        • app/Http/Controllers/Academy/QuestionController.php:411
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        Backtrace
        • app/Http/Controllers/Academy/QuestionController.php:451
        • app/Http/Controllers/Academy/QuestionController.php:411
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        • app/Http/Controllers/Academy/QuestionController.php:451
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        • app/Http/Controllers/Academy/QuestionController.php:411
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        Backtrace
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        • app/Http/Controllers/Academy/QuestionController.php:411
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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      2Category.php#?
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