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ভেক্টর পদ্ধতিতে 3ˆi+ˆj+ˆk এবং 2ˆi+2ˆj-ˆk এর ছেদ বিন্দুগামী সরলরেখার সমীকরণ নির্ণয় কর।

Created: 3 years ago | Updated: 3 months ago
Updated: 3 months ago
বাংলাদেশ প্রকৌশল ও প্রযুক্তি বিশ্ববিদ্যালয় (বুয়েট) শিক্ষাবর্ষঃ ২০১৭-২০১৮ উচ্চতর গণিত বিভিন্ন আকারের সরলরেখার সমীকরণ
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Best Ans:
10 months ago
MD.SOLAIMAN HOSAN

উচ্চতর গণিত

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m ঢাল এবং x - অক্ষের ছেদক অংশ b হলে সরলরেখার সমীকরণটি -
12x - 5y + 13 = 0 এর উপর লম্ব এবং মূলবিন্দুগামী সরলরেখা হবে-
5x-7y-9=0 সরলরেখা দ্বারা Y অক্ষ হতে খন্দিত অংশের মান কত হবে?
স্থানাঙ্কের অক্ষস্বরের সাথে সমান সমান কোণ উৎপন্নকারী সরলরেখা সমূহের ঢালের মান হবে-
  পরাবৃত্ত এবং y=x সরলরেখা দ্বারা আবদ্ধ ক্ষেত্রের ক্ষেত্রফল -
(-1, 2) এবং (4, -3) বিন্দুগামী সরলরেখা x অক্ষের যোগবোধক দিকের সাথে যে কোন উৎপন্ন করে তা হলো-
Promotion
Messages3TimelineExceptionsViews33RouteQueries28Models42Livewire0MailsGateSessionRequest
Request history8.2.27PHP Version66.28msRequest Duration10MBMemory UsageGET admission/single-questionRoute
  • warninglog[15:52:53] LOG.warning: htmlspecialchars_decode(): Passing null to parameter #1 ($string) of type st...
  • warninglog[15:52:53] LOG.warning: htmlspecialchars_decode(): Passing null to parameter #1 ($string) of type st...
  • warninglog[15:52:53] LOG.warning: htmlspecialchars_decode(): Passing null to parameter #1 ($string) of type st...
  • Booting (32ms)time
  • Application (34.27ms)time
  • 1 x Application (51.71%)
    34.27ms
    1 x Booting (48.28%)
    32.00ms
    33 templates were rendered
    • questions.mcq.single_questionsingle_question.blade.php#?blade
    • questions.include.show_timeshow_time.blade.php#?blade
    • questions.mode.readingreading.blade.php#?blade
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    • questions.mcq.sidebarsidebar.blade.php#?blade
    • common.modal.bookmark_modalbookmark_modal.blade.php#?blade
    • common.modal.tag_add_modaltag_add_modal.blade.php#?blade
    • common.modal.add_description_modaladd_description_modal.blade.php#?blade
    • common.modal.video_modalvideo_modal.blade.php#?blade
    • common.modal.edit_description_modaledit_description_modal.blade.php#?blade
    • common.modal.error_report_modalerror_report_modal.blade.php#?blade
    • job.job_include.job_scriptjob_script.blade.php#?blade
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    • common.script.follow_unfollow_scriptfollow_unfollow_script.blade.php#?blade
    • common.script.short_statistics_scriptshort_statistics_script.blade.php#?blade
    • layouts.single-question-appsingle-question-app.blade.php#?blade
    • includes.single_header_linksingle_header_link.blade.php#?blade
    • common.login_modallogin_modal.blade.php#?blade
    • components.authentication-card-logoauthentication-card-logo.blade.php#?blade
    • layouts.headerheader.blade.php#?blade
    • layouts.toolbartoolbar.blade.php#?blade
    • layouts.footerfooter.blade.php#?blade
    • common.includes.promotion_modalpromotion_modal.blade.php#?blade
    • common.includes.promotion_offcanvaspromotion_offcanvas.blade.php#?blade
    • includes.footer_link2footer_link2.blade.php#?blade
    • includes.restrictrestrict.blade.php#?blade
    • livewire-alert::components.scriptsscripts.blade.php#?blade
    • livewire-alert::components.flashflash.blade.php#?blade
    • admin.include.toastrtoastr.blade.php#?blade
    • common.search.search_scriptsearch_script.blade.php#?blade
    • common.script.promotion_scriptpromotion_script.blade.php#?blade
    • 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
    28 statements were executed5.3ms
    • QuestionController.php#190debugerror_satt340μsupdate `questions` set `view_count` = `view_count` + 1 where `id` = 99179
      Bindings
      • 0: 99179
      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
      • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
    • QuestionController.php#256debugerror_satt260μsselect `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` = '99179' and `questions`.`deleted_at` is null limit 1
      Bindings
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      • 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_satt130μsselect `id`, `question_id`, `option_1`, `option_2`, `option_3`, `option_4`, `option_5`, `image_option`, `image_question`, `answer` from `question_options` where `question_options`.`question_id` in (99179) and `question_options`.`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_satt170μsselect `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 (4108) 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_satt120μsselect `id`, `name`, `des_updated_by`, `des_added_by`, `link_subject_id`, `slug` from `subjects` where `subjects`.`id` in (74) 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_satt130μsselect `id`, `description`, `subject_id` from `subject_descriptions` where `subject_descriptions`.`subject_id` in (74) 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_satt190μsselect `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 (99179) and `subjectables`.`subjectable_type` = 'App\\Models\\Question' and `subjects`.`deleted_at` 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_satt120μsselect * from `vote_statistics` where `vote_statistics`.`question_id` in (99179)
      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_satt250μsselect * from `descriptions` where `descriptions`.`descriptionable_id` in (99179) and `descriptions`.`descriptionable_type` = 'App\\Models\\Question' and `status` in ('approve', 'active') and `descriptions`.`deleted_at` is null order by `vote` desc
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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`, `name`, `avatar` from `users` where `users`.`id` in (40209) 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_satt90μsselect `id`, `bookmarkable_id`, `bookmarkable_type`, `user_id` from `bookmarks` where `bookmarks`.`bookmarkable_id` in (99179) 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_satt90μsselect `id`, `votable_id`, `votable_type`, `user_id` from `votes` where `votes`.`votable_id` in (99179) 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_satt80μsselect `id`, `question_id`, `user_id`, `choosen_option` from `vote_logs` where `vote_logs`.`question_id` in (99179) 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_satt360μsselect `subjectable_id` from `subjectables` where `subjectable_type` = 'App\\Models\\Question' and `subject_id` in (2154)
      Bindings
      • 0: App\Models\Question
      • 1: 2154
      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_satt1.18msselect `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 (88399, 98544, 98561, 99179, 102524, 104293, 109972, 109997, 109999, 110162, 110771, 110963, 120825, 126383, 126624, 129428, 129618, 130126, 131374, 131389, 131684, 131766, 131786, 132332, 132728, 133908, 143484, 143936, 143989, 144598, 145403, 153941, 154219, 155195, 169255, 169376, 169457, 169460, 169782, 170908, 177933, 184142, 191485, 198241, 198654, 206856, 207977, 208060, 208251, 209825, 222056, 232793, 232797, 235358, 237001, 191268, 191805, 197735, 197903, 197974, 198192, 198196, 198242, 198423, 205679, 205772, 205864, 205974, 206074, 206155, 206160, 207968, 208139, 208253, 208493, 208568, 208574, 209816, 210068, 210080, 210154, 210174, 210287, 210293, 211818, 212983, 215907, 221989, 222046, 222050, 231227, 231308, 232452, 232764, 232766, 234685, 234909, 234979, 235350, 235458, 235567, 236479, 236483, 236493, 236567, 236573, 236655, 236895, 236898, 236997, 237000, 83720, 83728, 83839, 84187, 84190, 84202, 84579, 84908, 85101, 85114, 85192, 85209, 85249, 85250, 85360, 85421, 85495, 87296, 89834, 94242, 94362, 94464, 98119, 98126, 98204, 98434, 98440, 99110, 109984, 110332, 110547, 111075, 111719, 120574, 120636, 120967, 121074, 121075, 121758, 121762, 121849, 121853, 121856, 121962, 122056, 122147, 122247, 122428, 126381, 129595, 131024, 131045, 131121, 131205, 131299, 131302, 131375, 131679, 131697, 132294, 133573, 133595, 133711, 133726, 134205, 134215, 134751, 142203, 142742, 142743, 142937, 143572, 143718, 143721, 143943, 143987, 143990, 144256, 144382, 145292, 145668, 153985, 154901, 154938, 155171, 155172, 158681, 160652, 167637, 168369, 168919, 169465, 169560, 170744, 170915, 178827, 182473, 183525, 183847, 183983) and `id` != 99179 and `questions`.`deleted_at` is null order by `created_at` desc limit 6
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