Trong không gian Oxyz, cho đường thẳng \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiizaiaacQ % dadaWcaaqaaiaadIhacqGHsislcaaIYaaabaGaeyOeI0IaaGymaaaa % cqGH9aqpdaWcaaqaaiaadMhacqGHsislcaaIXaaabaGaaGOmaaaacq % GH9aqpdaWcaaqaaiaadQhaaeaacaaIYaaaaaaa!4341! d:\frac{{x - 2}}{{ - 1}} = \frac{{y - 1}}{2} = \frac{z}{2}\) và mặt phẳng \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca % WGqbaacaGLOaGaayzkaaGaaiOoaiaadIhacqGHRaWkcaaIYaGaamyE % aiabgkHiTiaadQhacqGHsislcaaI1aGaeyypa0JaaGimaaaa!4201! \left( P \right):x + 2y - z - 5 = 0\) . Tọa độ giao điểm của d và (P) là:
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Lời giải:
Báo saiTa có: \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaacQ % dadaWcaaqaaiaadIhacqGHsislcaaIYaaabaGaeyOeI0IaaGymaaaa % cqGH9aqpdaWcaaqaaiaadMhacqGHsislcaaIXaaabaGaaGOmaaaacq % GH9aqpdaWcaaqaaiaadQhaaeaacaaIYaaaaiabgkDiElaadsgacaGG % 6aWaaiqaaqaabeqaaiaadIhacqGH9aqpcaaIYaGaeyOeI0IaamiDaa % qaaiaadMhacqGH9aqpcaaIXaGaey4kaSIaaGOmaiaadshaaeaacaWG % 6bGaeyypa0JaaGOmaiaadshaaaGaay5EaaGaeyO0H4Taamytamaabm % aabaGaaGOmaiabgkHiTiaadshacaGG7aGaaGymaiabgUcaRiaaikda % caWG0bGaai4oaiaaikdacaWG0baacaGLOaGaayzkaaaaaa!63FC! d:\frac{{x - 2}}{{ - 1}} = \frac{{y - 1}}{2} = \frac{z}{2} \Rightarrow d:\left\{ \begin{array}{l} x = 2 - t\\ y = 1 + 2t\\ z = 2t \end{array} \right. \Rightarrow M\left( {2 - t;1 + 2t;2t} \right)\) là một điểm thuộc đường thẳng d.
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGnb % Gaeyypa0JaamizaiabgMIihpaabmaabaGaamiuaaGaayjkaiaawMca % aiabgkDiElaaikdacqGHsislcaWG0bGaey4kaSIaaGOmamaabmaaba % GaaGymaiabgUcaRiaaikdacaWG0baacaGLOaGaayzkaaGaeyOeI0Ya % aeWaaeaacaaIYaGaamiDaaGaayjkaiaawMcaaiabgkHiTiaaiwdacq % GH9aqpcaaIWaaabaGaeyi1HSTaamiDaiabg2da9iaaigdacqGHshI3 % caWGnbWaaeWaaeaacaaIXaGaai4oaiaaiodacaGG7aGaaGOmaaGaay % jkaiaawMcaaaaaaa!5D47! \begin{array}{l} M = d \cap \left( P \right) \Rightarrow 2 - t + 2\left( {1 + 2t} \right) - \left( {2t} \right) - 5 = 0\\ \Leftrightarrow t = 1 \Rightarrow M\left( {1;3;2} \right) \end{array}\)
Đề thi thử tốt nghiệp THPT QG môn Toán năm 2020
Tuyển chọn số 4