Cho ba vectơ a, b, c được biểu diễn như Hình 9

Lời giải Khám phá 2 trang 90 Toán 10 sách Chân trời sáng tạo hay nhất, chi tiết sẽ giúp học sinh dễ dàng làm bài tập Toán 10.

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Giải bài tập Toán 10 Bài 2: Tổng và hiệu của hai vectơ

Khám phá 2 trang 90 Toán lớp 10 Tập 1Cho ba vectơ a with rightwards arrow on top comma text   end text b with rightwards arrow on top comma text   end text c with rightwards arrow on top được biểu diễn như Hình 9.

Giải Toán 10 Bài 2: Tổng và hiệu của hai vectơ - Chân trời sáng tạo (ảnh 1)

Hãy hoàn thành các phép cộng vectơ sau và so sánh các kết quả tìm được:

a) a with rightwards arrow on top plus b with rightwards arrow on top equals stack A B with rightwards arrow on top plus stack B C with rightwards arrow on top equals box enclose ?;

    b with rightwards arrow on top plus a with rightwards arrow on top equals stack A E with rightwards arrow on top plus stack E C with rightwards arrow on top equals box enclose ?

b) open parentheses a with rightwards arrow on top plus b with rightwards arrow on top close parentheses plus c with rightwards arrow on top equals open parentheses stack A B with rightwards arrow on top plus stack B C with rightwards arrow on top close parentheses plus stack C D with rightwards arrow on top equals stack A C with rightwards arrow on top plus stack C D with rightwards arrow on top equals box enclose ?;

    a with rightwards arrow on top plus open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses equals stack A B with rightwards arrow on top plus open parentheses stack B C with rightwards arrow on top plus stack C D with rightwards arrow on top close parentheses equals stack A B with rightwards arrow on top plus stack B D with rightwards arrow on top equals box enclose ?

Lời giải:

a) Ta có: a with rightwards arrow on top plus b with rightwards arrow on top equals stack A B with rightwards arrow on top plus stack B C with rightwards arrow on top equals stack A C with rightwards arrow on top.

b with rightwards arrow on top plus a with rightwards arrow on top equals stack A E with rightwards arrow on top plus stack E C with rightwards arrow on top equals stack A C with rightwards arrow on top.

Do đó a with rightwards arrow on top plus b with rightwards arrow on top equals b with rightwards arrow on top plus a with rightwards arrow on top.

b) Ta có: open parentheses a with rightwards arrow on top plus b with rightwards arrow on top close parentheses plus c with rightwards arrow on top equals open parentheses stack A B with rightwards arrow on top plus stack B C with rightwards arrow on top close parentheses plus stack C text D end text with rightwards arrow on top equals stack A C with rightwards arrow on top plus stack C text D end text with rightwards arrow on top equals stack A text D end text with rightwards arrow on top.

a with rightwards arrow on top plus open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses equals stack A B with rightwards arrow on top plus open parentheses stack B C with rightwards arrow on top plus stack C text D end text with rightwards arrow on top close parentheses equals stack A B with rightwards arrow on top plus stack text BD end text with rightwards arrow on top equals stack A text D end text with rightwards arrow on top.

Do đó open parentheses a with rightwards arrow on top plus b with rightwards arrow on top close parentheses plus c with rightwards arrow on top equals a with rightwards arrow on top plus open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses.

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