- #1
Nusc
- 760
- 2
Homework Statement
B = grad(A)
Find A
If one is given B z-hat
Homework Equations
The Attempt at a Solution
What mathematical operation would I apply to solve this?
HallsofIvy said:By "one is given B z-hat" do you mean you are given only the z-component of grad A?
Then there are many solutions. For example, if we are given that the z-component of grad A, then A can be any function of x,y- as long as it has no dependence on z, the z-component of grad A is 0.
Nusc said:SOrry folks I meant Curl
A cross product is a mathematical operation that takes two vectors as inputs and produces a third vector that is perpendicular to both of the input vectors. It is denoted by the symbol "x" or "⨯" and the result is sometimes referred to as the vector product.
To solve for a given B in the z-hat direction, you will need to use the cross product formula: A x B = |A| |B| sinθ, where A is the first vector, B is the second vector, and θ is the angle between them. In this case, you will set θ to 90 degrees since the vector B is in the z-hat direction. Then, rearrange the formula to solve for B.
Cross products are commonly used in physics and engineering to calculate torque, magnetic fields, and angular momentum. They are also used in computer graphics and animation to create 3D effects and rotations.
Yes, you can still use the cross product formula to solve for a given B even if the vectors are not perpendicular. However, the resulting vector will not be in the z-hat direction and will have a magnitude and direction determined by the angle between the two input vectors.
Yes, there are other methods for finding a cross product such as using determinant matrices or using the properties of cross products, such as the fact that the result is perpendicular to both input vectors. However, using the formula is the most direct and common method for solving for a given B in the z-hat direction.