# Math Help - Vector Operations

1. ## Vector Operations

Can somebody check the following answers are correct and give any guidance on the others?

I was given F = (x^3, By^2, xyz)

(i) del.F = 3x^2 + 2By + xy

(ii) del.(del.F) = 6x + 2B // Differentiating (i)

(iii) del x F = (xz)i - (yz)j

(iv) del x (del x F)
Not sure how to do this?

(v) del^2(F)
Do you just differentiate F twice wrt x,y,z and then add them?

(vi) (F.del).F
Summation convention?

2. Originally Posted by Yerobi
Can somebody check the following answers are correct and give any guidance on the others?

I was given F = (x^3, By^2, xyz)

(i) del.F = 3x^2 + 2By + xy

(ii) del.(del.F) = 6x + 2B // Differentiating (i)
$\nabla(\nabla.{\b{F}})=\left[\frac{\partial}{\partial x}(\nabla.{\b{F}}),\ \frac{\partial}{\partial y}(\nabla.{\b{F}}),\ \frac{\partial}{\partial z}(\nabla.{\b{F}})
\right]
$

(gradient of divergence of F) is a vector.

RonL