- #1
shedrick94
- 30
- 0
I've got ∇×(∇×R)=∇(∇.R)-∇2R [call it eq.1]
However I have the identity ∇×(A×B)=A(∇.B)-B(∇⋅A)+ (B⋅∇)A-(A⋅∇)B [call it eq.2]
Substituting in A=∇ and R=B into eq.2 we get ∇×(∇×R)=∇(∇.R)-R(∇⋅∇)+ (R⋅∇)∇-(∇⋅∇)R
which i work out to be ∇×(∇×R)=∇(∇.R)-R(∇⋅∇)+ (R⋅∇)∇-∇2R
Basically I don't understand what happens to the two terms -R(∇⋅∇)+ (R⋅∇)∇ from eq.2 when we get to eq.1, why do they disappear?
However I have the identity ∇×(A×B)=A(∇.B)-B(∇⋅A)+ (B⋅∇)A-(A⋅∇)B [call it eq.2]
Substituting in A=∇ and R=B into eq.2 we get ∇×(∇×R)=∇(∇.R)-R(∇⋅∇)+ (R⋅∇)∇-(∇⋅∇)R
which i work out to be ∇×(∇×R)=∇(∇.R)-R(∇⋅∇)+ (R⋅∇)∇-∇2R
Basically I don't understand what happens to the two terms -R(∇⋅∇)+ (R⋅∇)∇ from eq.2 when we get to eq.1, why do they disappear?