Formulas in vector analysis. Here is a collection of formulas in vector analysis. Have a look!!
Collection of formulas in vector analysis
As the heading says, here I have listed the formulas in vector analysis. And I have already used these formulas. But the list is not a comprehensive one. I’ll keep on updating it.
Scalar & vector triple product
Let’s suppose that I have three vectors so that
Now comes the formula for the scalar triple product of these three vectors.
The scalar triple product of these three vectors is . And the formula for will be
Also, it’s good to remember that
Now these three vectors will be coplanar if
Next, comes the formula for the vector triple product of these three vectors.
The vector triple product of these three vectors is or .
Now comes the formulas. So these are as follows:
Differentiation & integration of vectors
Suppose there’s a vector as
And are all functions of . Thus is also a function of .
Therefore will be
Again suppose the vector is
If I want to integrate it in between and where , it will be
Application of differentiation of vectors
An unit tangent vector () of any vector is
Gradient vector of a scalar function is written as
And the formula is
Application of gradient vector
If is a scalar function and is a given vector, the directional derivative of the scalar function at a specific point will be
Here is the unit vector of the given vector. Also, is the gradient vector of the scalar function at the particular point.
The unit normal vector () to any surface is
Also, is the gradient vector pf the surface at a specific point. and is the magnitude of the gradient vector at that specific point.