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单词 scalar triple product
释义

scalar triple product

The scalar triple product of three vectors a, b, and c, is a·(b×c), the scalar product of a with the vector product b×c. It is a scalar quantity and is denoted [a,b,c]. It has the following properties:

(i) [a,b,c] = −[a,c,b].
(ii) [a,b,c] = [b,c,a] = [c,a,b].
(iii) The vectors a, b, and c are linearly dependent if and only if [a,b,c] = 0.
(iv) If a = (a1,a2,a3), etc., then

(v) Let inline, inline, and inline represent a, b and c. Then the parallelepiped with OA, OB, and OC as three of its edges has volume equal to the absolute value of [a,b,c].
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更新时间:2025/5/20 3:49:08