What is scalar triple product of vector?
The scalar triple product of three vectors a, b, and c is (a×b)⋅c. The scalar triple product is important because its absolute value |(a×b)⋅c| is the volume of the parallelepiped spanned by a, b, and c (i.e., the parallelepiped whose adjacent sides are the vectors a, b, and c).
Which is the vector triple product?
Vector Triple Product Properties The cross-product of the vectors such as a × (b × c) and (a × b) × c is known as the vector triple product of a, b, c. The ‘r’ vector r=a×(b×c) is perpendicular to a vector and remains in the b and c plane.
What is the difference between scalar triple product and vector triple product?
where B × C is the cross product of two vectors (resulting into a vector) and the dot indicates the inner product between two vectors (a scalar). The triple product is sometimes called the scalar triple product to distinguish it from the vector triple product A×(B×C).
What is a scalar triple product?
The scalar triple product (also called the mixed product, box product, or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two.
What is meant by scalar triple product?
By the name itself, it is evident that the scalar triple product of vectors means the product of three vectors. It means taking the dot product of one of the vectors with the cross product of the remaining two. It is denoted as. [a b c ] = ( a × b) .
What is BAC cab rule?
linear-algebra vectors. These are examples of BAC-CAB rule in a physics book.( →A×→B)⋅(→C×→D)=(→A⋅→C)(→B⋅→D)−(→A⋅→D)(→B⋅→C) →A×(→B×(→C×→D))=→B(→A⋅(→C×→D))−(→A⋅→B)(→C⋅→D)
What property is AxB BxA?
Commutative property
Mathematics Glossary » Table 3
| Associative property of addition | (a +b) + c = a + (b+c) |
|---|---|
| Associative property of multiplication | (a x b) x c = a x (b x c) |
| Commutative property of multplication | a x b = b x a |
| Multiplicative identity property 1 | a x 1 = 1 x a = a |
What is meant by coplanar vectors?
Coplanar vectors are defined as vectors which are lying on the same in a three-dimensional plane. The vectors are parallel to the same plane. It is always easy to find any two random vectors in a plane, which are coplanar.