Page 147 - 《數學觀念總整理 3-4 》- 2019版

四十一、外積

1. 外積 ( )

⃑
⃑
 給 個向量，求 × = ？
ex ∶ 一個例子

⃑ = ( 1, 2, 3 )
11
⃑
= ( 1, 1, 1 )

⃑
(1) ⃑ × = (2 − 3, 3 − 1,1 − 2 ) = (−1, 2, −1)
⃑

(2) ⃑ × = (−1) + 2 + (−1) = √ 6
(−1, 2, −1) ∙ (1, 2, 3) = −1 + 4 − 3 = 0
check ∶ ， OK!
(−1, 2, −1) ∙ (1, 1, 1) = −1 + 2 − 1 = 0

 外積 ( ) 算法

⃑ = ( , , )

⃑
= ( , , )

⃑
⟹ ⃑ × = , ,

( , , ) ∙ , , = 0

⎛
check ∶
⎜

( , , ) ∙ , , = 0
⎝

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