Cho hình lăng trụ đứng ABC.A'B'C' có đáy là tam giác ABC vuông tại A có BC = 2a, \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaiaadk % eacqGH9aqpcaWGHbWaaOaaaeaacaaIZaaaleqaaaaa!3A44! AB = a\sqrt 3 \) . Khoảng cách từ (AA') đến mặt phẳng (BCC'B') là:
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Lời giải:
Báo saiTa có \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaiqadg % eagaqbaiaab+cacaqGVaWaaeWaaeaacaWGcbGaam4qaiqadoeagaqb % aiqadkeagaqbaaGaayjkaiaawMcaaaaa!3DAE! AA'{\rm{//}}\left( {BCC'B'} \right)\) nên khoảng cách từ AA' đến mặt phẳng (BCC'B') cũng chính là khoảng cách từ A đến mặt phẳng (BCC'B').
Hạ \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaiaadI % eacqGHLkIxcaWGcbGaam4qaiabgkDiElaadgeacaWGibGaeyyPI41a % aeWaaeaacaWGcbGaam4qaiqadoeagaqbaiqadkeagaqbaaGaayjkai % aawMcaaaaa!4526! AH \bot BC \Rightarrow AH \bot \left( {BCC'B'} \right)\)
Ta có : \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIXaaabaGaamyqaiaadIeadaahaaWcbeqaaiaaikdaaaaaaOGaeyyp % a0ZaaSaaaeaacaaIXaaabaGaamyqaiaadkeadaahaaWcbeqaaiaaik % daaaaaaOGaey4kaSYaaSaaaeaacaaIXaaabaGaamyqaiaadoeadaah % aaWcbeqaaiaaikdaaaaaaOGaeyypa0ZaaSaaaeaacaaIXaaabaGaaG % 4maiaadggadaahaaWcbeqaaiaaikdaaaaaaOGaey4kaSYaaSaaaeaa % caaIXaaabaGaamOqaiaadoeadaahaaWcbeqaaiaaikdaaaGccqGHsi % slcaWGbbGaamOqamaaCaaaleqabaGaaGOmaaaaaaGccqGH9aqpdaWc % aaqaaiaaigdaaeaacaaIZaGaamyyamaaCaaaleqabaGaaGOmaaaaaa % GccqGHRaWkdaWcaaqaaiaaigdaaeaacaWGHbWaaWbaaSqabeaacaaI % Yaaaaaaakiabg2da9maalaaabaGaaGinaaqaaiaaiodacaWGHbWaaW % baaSqabeaacaaIYaaaaaaaaaa!5A13! \frac{1}{{A{H^2}}} = \frac{1}{{A{B^2}}} + \frac{1}{{A{C^2}}} = \frac{1}{{3{a^2}}} + \frac{1}{{B{C^2} - A{B^2}}} = \frac{1}{{3{a^2}}} + \frac{1}{{{a^2}}} = \frac{4}{{3{a^2}}}\)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H4Taam % yqaiaadIeacqGH9aqpdaWcaaqaaiaadggadaGcaaqaaiaaiodaaSqa % baaakeaacaaIYaaaaaaa!3D7D! \Rightarrow AH = \frac{{a\sqrt 3 }}{2}\)
Vậy khoảng cách từ (AA') đến mặt phẳng (BCC'B') bằng \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % WGHbWaaOaaaeaacaaIZaaaleqaaaGcbaGaaGOmaaaaaaa!3887! \frac{{a\sqrt 3 }}{2}\)
Đề thi thử tốt nghiệp THPT QG môn Toán năm 2020
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