# Vector Operations

• February 28th 2008, 11:13 AM
Yerobi
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?
• February 29th 2008, 03:02 AM
CaptainBlack
Quote:

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