A student writes the following script for a scene in a futuristic movie.
1 answer:
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- The length of the cross product of two vectors
- The scalar triple product of the vectors a, b, and c
- The volume of the parallelepiped determined by the vectors a, b, and c is the magnitude of their scalar triple product.
<u>Explanation</u>:
- The length of the cross product of two vectors is
| a
b | = |a| |b| sin θ
- The length of the cross product of two vectors is equal to the area of the parallelogram determined by the two vectors (see figure below).
- Anticommutativity:
| a b | = - | b
a |
- Multiplication by scalars:
(ca) b = c (a
b) = a
(cb)
- Distributivity:
a (b + c) = (a
b) + (a
c)
- The scalar triple product of the vectors a, b, and c:
a . (b c) = (a
b) . c
- The magnitude of the scalar triple product is the volume of the parallelepiped of the vectors a, b, and c.
- The vector triple product of the vectors a, b, and c is given as
a (b
c) = (a.c) b - (a.b)
c