curl

**scubasteve123** · December 15th 2009, 05:12 PM

Find curl(a X f )
a=a(sub1) i + a(sub2) j +a(sub3) k
f=x i + y j +z k

**pickslides** · December 15th 2009, 05:26 PM

If memory serves then

$ \left| \begin{array}{ccc} i & j & k \\ a_1 & a_2 & a_3 \\ x & y & z \end{array} \right|= i(a_2z-a_3y)-j(a_1z-a_3x)+k(a_1y-a_2x)$

**HallsofIvy** · December 16th 2009, 02:21 AM

Originally Posted by pickslides

If memory serves then

$ \left| \begin{array}{ccc} i & j & k \\ a_1 & a_2 & a_3 \\ x & y & z \end{array} \right|= i(a_2z-a_3y)-j(a_1z-a_3x)+k(a_1y-a_2x)$

That is $a\times f$ . scubasteve123 still needs to take the curl.

But it is far simpler to recognise that, because a is a constant vector,
$\nabla\times (a\times f)= a\times (\nabla\times f)$ .

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