Mark44 said:As you've written it, the expression doesn't make any sense. If you calculate (a - b) [itex]\cdot[/itex] (b - c), you get a scalar, which you can't cross with a vector. Do you mean
(a - b) [itex]\cdot[/itex] ((b - c) X (c - a))?
If so, here's a Wikipedia article that might be of help to you - http://en.wikipedia.org/wiki/Scalar_triple_product#Scalar_triple_product
Vector calculus is a branch of mathematics that deals with the study of vector fields and their properties. It involves the use of vectors and their operations, such as addition, subtraction, and dot and cross products, to analyze and manipulate functions that have multiple variables.
Simplifying expressions in vector calculus is important because it allows for a clearer understanding of the underlying concepts and relationships between different variables. It also helps in solving complex problems and making calculations more efficient.
Some common techniques used to simplify vector calculus expressions include simplifying fractions, factoring, combining like terms, and using trigonometric identities. It is also important to understand the properties of vectors and their operations, which can help in simplifying expressions.
Simplifying expressions can make it easier to analyze and solve real-world problems that involve vector calculus, such as in physics, engineering, and economics. It can also help in visualizing and interpreting the results of vector calculus calculations.
Some tips for simplifying vector calculus expressions include practicing regularly, understanding the properties and rules of vector operations, and breaking down complex expressions into smaller, more manageable parts. It is also helpful to double-check calculations and simplify expressions as much as possible before moving on to the next step.