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Cách phân tích một vecto theo các vecto cho trước - Toán 12

1. Cách phân tích một vecto theo các vecto cho trước

Để phân tích vecto \(\overrightarrow x \) theo các vecto \(\overrightarrow {{x_1}} \), \(\overrightarrow {{x_2}} \),…, \(\overrightarrow {{x_n}} \) cho trước, ta chèn các điểm để xuất hiện \(\overrightarrow {{x_1}} \), \(\overrightarrow {{x_2}} \),…, \(\overrightarrow {{x_n}} \) và biến đổi đến khi nào chỉ còn \(\overrightarrow {{x_1}} \), \(\overrightarrow {{x_2}} \),…, \(\overrightarrow {{x_n}} \) và các hệ số của chúng.

2. Ví dụ minh hoạ

Cho tứ diện ABCD. Đặt \(\overrightarrow {AB}  = \overrightarrow a \), \(\overrightarrow {AC}  = \overrightarrow b \), \(\overrightarrow {AD}  = \overrightarrow c \). Gọi M là trung điểm của đoạn thẳng BC. Phân tích \(\overrightarrow {DM} \) theo các vecto \(\overrightarrow a \), \(\overrightarrow b \), \(\overrightarrow c \).

Giải:

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