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## Homework Statement

derive the identity:

del((

**F**)^2) = 2

**F**. del(

**F**) + 2

**F**x (del x

**F**)

the dot is a dot product

## Homework Equations

## The Attempt at a Solution

first i set

**F**= <a,b,c>, making

**F**^2 = a^2 + b^2 + c^2

I took the partial derivatives with respect to x, y, and z (to get the necessary parts for the gradient), which gives me:

d/dx(a^2 + b^2 + c^2) = 2a * da/dx + 2b*db/dx + 2c*db/dc

d/dy(...) = ... 2a * da/dy + 2b*db/dy + 2c*db/dy

d/dz(...) = ... 2a * da/dz + 2b*db/dz + 2c*db/dz

But, because its a gradient of a scalar, the three components above are those of a vector. After putting together the components I am not sure where to go. What actually confuses me is that in the derivation you are supposed to show that a vector equals a vector plus a scalar -- the ( 2F . del(F)) term is a scalar... . If someone could please help me out that would be greatly appreciated. Thank you