Scalar Triple Product

Vector is said to be a quantity that helps to represent through forms of magnitude and direction. This vector may either look like an arrow which may point towards any direction of object.

The scalar triple product of three vectors a, b and c is represented as (a × b) ⋅c. This is said to be a scalar product, which is similar to that of dot product and helps to evaluate to single number. The scalar product turns out to be an important aspect as it comes with absolute value | (a × b) ⋅c| which is said to be the volume of parallelepiped spanned by a, b and c.

The triple product is known to be an important concept when it comes to vector calculus. This product has three vectors and is defined in three dimensions. There are two different types of triple products:

1. Scalar triple product
2. Vector triple product

Properties of scalar triple product

1. The position of operators can be shifted without changing the order of operands. Therefore, it helps to keep the value of product:

x⃗.(y⃗ x z⃗) = (x⃗ x y⃗). z⃗

2. The value of scalar triple product does not change in case the operands undergo any circular shift:

x⃗.(y⃗ x z⃗) = y⃗. (z⃗ x x⃗) = z⃗. (x⃗ x y⃗)

3. While swapping two vectors, the scalar triple product is negative

x⃗. (y⃗x z⃗ ) = – x⃗. (z⃗ x y⃗)

4. The scalar triple product turns out to be equal to that of determinant of components of any vector that is involved

a⃗.(b⃗ ×c⃗ )= a_x  a_ya_z

b_x b_yb_z

c_x   c_yc_z

Links of Previous Main Topic:-

• Introduction to statics
• Introduction to vector algebra
• Magnitude of a vector
• Product of vector a by scalar m
• Addition of vectors
• Subtraction of vectors
• Addition of vectors using polygon method
• Resolution of vectors
• Unit vectors
• Scalar or dot product of two vectors

Links of Next Mechanical Engineering Topics:-

• Introduction concept of equilibrium of rigid body
• Friction introduction
• Introduction about distributed forces