Toán Lớp 10: giúp em với em đang cần gấp ạ, em cảm ơn. cho ngũ giác ABCDE, chứng minh rằng: a) vectơ AB + vectơ CD + vectơ BC + vectơ DE + vectơ EA

Question

Toán Lớp 10:  giúp em với em đang cần gấp ạ, em cảm ơn. cho ngũ giác ABCDE, chứng minh rằng: a) vectơ AB + vectơ CD + vectơ BC + vectơ DE + vectơ EA = vectơ 0 b) vectơ AB + vectơ ED + vectơ BE = vectơ ED - vectơ EA

thanhtung · Answer

Giải đáp:   a) Ta c&oacute;:             &minus;  &minus;  &rarr;        A    B        +        &minus;  &minus;  &rarr;        C    D        +        &minus;  &minus;  &rarr;        B    C        +        &minus;  &minus;  &rarr;        D    E        =    (        &minus;  &minus;  &rarr;        A    B        +        &minus;  &minus;  &rarr;        B    C        )    +    (        &minus;  &minus;  &rarr;        C    D        +        &minus;  &minus;  &rarr;        D    E        )     AB&rarr;+CD&rarr;+BC&rarr;+DE&rarr;=(AB&rarr;+BC&rarr;)+(CD&rarr;+DE&rarr;)            =        &minus;  &minus;  &rarr;        A    C        +        &minus;  &minus;  &rarr;        C    E        =        &minus;  &minus;  &rarr;        A    E         =AC&rarr;+CE&rarr;=AE&rarr;            &rArr;        &minus;  &minus;  &rarr;        A    B        +        &minus;  &minus;  &rarr;        C    D        =        &minus;  &minus;  &rarr;        A    E        &minus;        &minus;  &minus;  &rarr;        B    C        &minus;        &minus;  &minus;  &rarr;        D    E         &rArr;AB&rarr;+CD&rarr;=AE&rarr;&minus;BC&rarr;&minus;DE&rarr;      (đpcm)   b)             &minus;  &minus;  &rarr;        A    B        +        &minus;  &minus;  &rarr;        D    C        +        &minus;  &minus;  &rarr;        B    E        +        &minus;  &minus;  &rarr;        E    D        =    (        &minus;  &minus;  &rarr;        A    B        +        &minus;  &minus;  &rarr;        B    E        )    +    (        &minus;  &minus;  &rarr;        E    D        +        &minus;  &minus;  &rarr;        D    C        )     AB&rarr;+DC&rarr;+BE&rarr;+ED&rarr;=(AB&rarr;+BE&rarr;)+(ED&rarr;+DC&rarr;)            =        &minus;  &minus;  &rarr;        A    E        +        &minus;  &minus;  &rarr;        E    C        =        &minus;  &minus;  &rarr;        A    C         =AE&rarr;+EC&rarr;=AC&rarr;            &rArr;        &minus;  &minus;  &rarr;        A    B        =        &minus;  &minus;  &rarr;        A    C        &minus;        &minus;  &minus;  &rarr;        D    C        &minus;        &minus;  &minus;  &rarr;        B    E        &minus;        &minus;  &minus;  &rarr;        E    D         &rArr;AB&rarr;=AC&rarr;&minus;DC&rarr;&minus;BE&rarr;&minus;ED&rarr;      (đpcm)             &minus;  &minus;  &rarr;          :đ&aacute;ng ra mấy c&aacute;i n&agrave;y ở tr&ecirc;n đầu của chữ cơ , nhưng ko lm đc n&ecirc;n đ&agrave;nh phải vậy

maitrucloan · Answer

Giải đáp:       Lời giải và giải thích chi tiết:   Lời giải:   a) Ta c&oacute;:             &minus;  &minus;  &rarr;        A    B        +        &minus;  &minus;  &rarr;        C    D        +        &minus;  &minus;  &rarr;        B    C        +        &minus;  &minus;  &rarr;        D    E        =    (        &minus;  &minus;  &rarr;        A    B        +        &minus;  &minus;  &rarr;        B    C        )    +    (        &minus;  &minus;  &rarr;        C    D        +        &minus;  &minus;  &rarr;        D    E        )     AB&rarr;+CD&rarr;+BC&rarr;+DE&rarr;=(AB&rarr;+BC&rarr;)+(CD&rarr;+DE&rarr;)            =        &minus;  &minus;  &rarr;        A    C        +        &minus;  &minus;  &rarr;        C    E        =        &minus;  &minus;  &rarr;        A    E         =AC&rarr;+CE&rarr;=AE&rarr;            &rArr;        &minus;  &minus;  &rarr;        A    B        +        &minus;  &minus;  &rarr;        C    D        =        &minus;  &minus;  &rarr;        A    E        &minus;        &minus;  &minus;  &rarr;        B    C        &minus;        &minus;  &minus;  &rarr;        D    E         &rArr;AB&rarr;+CD&rarr;=AE&rarr;&minus;BC&rarr;&minus;DE&rarr;      (đpcm)   b)             &minus;  &minus;  &rarr;        A    B        +        &minus;  &minus;  &rarr;        D    C        +        &minus;  &minus;  &rarr;        B    E        +        &minus;  &minus;  &rarr;        E    D        =    (        &minus;  &minus;  &rarr;        A    B        +        &minus;  &minus;  &rarr;        B    E        )    +    (        &minus;  &minus;  &rarr;        E    D        +        &minus;  &minus;  &rarr;        D    C        )     AB&rarr;+DC&rarr;+BE&rarr;+ED&rarr;=(AB&rarr;+BE&rarr;)+(ED&rarr;+DC&rarr;)            =        &minus;  &minus;  &rarr;        A    E        +        &minus;  &minus;  &rarr;        E    C        =        &minus;  &minus;  &rarr;        A    C         =AE&rarr;+EC&rarr;=AC&rarr;            &rArr;        &minus;  &minus;  &rarr;        A    B        =        &minus;  &minus;  &rarr;        A    C        &minus;        &minus;  &minus;  &rarr;        D    C        &minus;        &minus;  &minus;  &rarr;        B    E        &minus;        &minus;  &minus;  &rarr;        E    D         &rArr;AB&rarr;=AC&rarr;&minus;DC&rarr;&minus;BE&rarr;&minus;ED&rarr;      (đpcm)