Vectors

Question 1

What is the curl of a vector?

Answer 1

It can be described as the representation of the magnitude and direction of a rotating vector field.

∇×f = i(∂f_z/∂y - ∂f_y/∂z) -j(∂f_z/∂x - ∂f_x/∂z) +k(∂f_y/∂x - ∂f_x/∂y)

Question 2

What is a vector said to be Irrotational?

Answer 2

When the curl (∇ x f) is zero.

Question 3

What is the divergence of a vector?

Answer 3

Expressed as divf or ∇•f, the divergence of a vector f(x,y,z) is given as, :

∂F_x/∂x + ∂F_y/∂y + ∂F_z/∂z

Question 4

When is a vector said to be solenoidal?

Answer 4

It is said to be solenoidal if all the divergence of all the points gives zero before the values from a given point are plugged in. That is, ∂F_x/∂x = 0, ∂F_y/∂y = 0, and ∂F_z/∂z = 0

Question 5

What is the formula for Laplacian of Scalar?

Answer 5

Laplacian of Scalar (∇²f) is given as:
∂²Φ/∂x² + ∂²Φ/∂y² + ∂²Φ/∂z²