Calculus Volume 3 · free preview
The Cross Product
The cross product of two vectors is a perpendicular vector whose magnitude is the parallelogram area and whose direction follows the right-hand rule, computed by a determinant and applied to torque and planes.
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.
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