Solving Vector Identity: {phi (grad phi)} X (n^)dS=0

Thread starter Kolahal Bhattacharya
Start date Mar 8, 2007
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Identity Vector Vector identity

In summary, a vector identity is an equation used in physics and engineering to relate different vector quantities. It simplifies and solves complex problems involving vectors. One example is {phi (grad phi)} X (n^)dS=0, which represents the cross product of two vectors that are perpendicular to each other. Vector identity is used to simplify and solve problems by reducing complex equations to simpler forms. Solving {phi (grad phi)} X (n^)dS=0 helps determine the relationship between the two vectors and can lead to solutions for more complex vector equations. Additionally, there are other frequently used vector identities in science, such as dot product, triple product, and vector calculus identities. These are crucial in solving various problems

Mar 8, 2007

Kolahal Bhattacharya

Homework Statement

I am to show: closed integral {phi (grad phi)} X (n^)dS=0

Homework Equations

The Attempt at a Solution

I understand I am to use divergence theorem here.but cannot approach.Please help

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Mar 8, 2007

Dick

Science Advisor

Homework Helper

Is 'X' supposed to mean a cross product between the normal vector and the gradient?

Mar 8, 2007

Kolahal Bhattacharya

yes.It means that.

Mar 9, 2007

Dick

Science Advisor

Homework Helper

Try using [tex]\int_S n \times a dS = \int_V curl(a) dV[/tex].

Last edited: Mar 9, 2007

1. What is a vector identity?

A vector identity is an equation that relates different vector quantities to each other. It is often used in physics and engineering to simplify and solve complex problems involving vectors.

2. What is the meaning of {phi (grad phi)} X (n^)dS=0 in the context of vector identity?

This equation represents the cross product of the vector {phi (grad phi)} and the normal vector (n^)dS, which is equal to zero. This means that the two vectors are perpendicular to each other, and their cross product has a magnitude of zero.

3. How is vector identity used in solving problems?

Vector identity is used to simplify and solve problems involving vectors. By manipulating and applying these identities, complex vector equations can be reduced to simpler forms, making them easier to solve.

4. What is the significance of solving {phi (grad phi)} X (n^)dS=0?

Solving this equation is significant because it allows us to determine the relationship between the vector {phi (grad phi)} and the normal vector (n^)dS. It can also help us find solutions to more complex vector equations that involve these vectors.

5. Are there other vector identities that are frequently used in science?

Yes, there are many other vector identities that are commonly used in science, such as the dot product identities, the triple product identities, and the vector calculus identities. These identities are essential for solving a wide range of problems in physics, engineering, and mathematics.