Calculus Volume 3 · 免费预览
叉积
两个向量的叉积是一个与二者垂直的向量，其大小等于平行四边形的面积，其方向遵循右手定则；叉积通过行列式计算，可用于力矩与平面。
1. Definition and the determinant
Definition and the determinant
2. Computing and applications
Computing and applications
3. The scalar triple product and planes
The scalar triple product and planes
4. The cross product's magnitude as area
The cross product's magnitude as area
5. Cross product direction
The cross product u cross v is which kind of vector?
6. Magnitude meaning
The magnitude |u cross v| equals which geometric quantity?
7. Determinant computation
The cross product (1, 2, 3) cross (4, 5, 6) equals which vector?
8. Parallel vectors
The cross product of two parallel vectors equals what?
9. Non-associativity
The cross product fails to be associative. What does u cross (v cross w) typically differ from?
10. Torque formula
Torque equals the position vector crossed with which other vector? Answer with one word.
11. Triple product volume
The scalar triple product u dot (v cross w) gives the volume of which solid? Answer with one word.
12. Anticommutative flip
u cross v equals negative of which reversed product? Answer like v cross u.
13. Coplanarity test
Three vectors are coplanar when which product vanishes?
14. Triangle area factor
The area of the triangle spanned by u and v is half of what product's magnitude? Answer like u cross v.