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user41048 3 weeks ago
### Is cross product of del ∇ x ∇ is zero in vectors?

I came across a vector term like

```
∇(∇ X F) = 0
```

So I though to solve it like

```
M = ∇.(∇ x F)
= F .( ∇ x ∇) - ∇.(∇ X F )
= F .( ∇ x ∇) - M
2M = F .( ∇ x ∇) = 0 **(Here I suppose ∇ x ∇ must be ZERO)** .
```

so

```
∇(∇ X F) =0
```

Is this is true that `∇ x ∇ = 0`

?

From Wikipedia,

If two vectors have the same direction (or have the exact opposite direction from one another, i.e. are not linearly independent) or if either one has zero length, then their cross product is zero.

Asked in 3 weeks ago

Viewed 3,991 times

Voted 6

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Viewed 3,991 times

Voted 6

Answered 1 times