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

and

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:

and

**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**

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**

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.

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