Re: [工數] (a constant vector cross del) cross r
※ 引述《sa12e3 ((．＿．?))》之銘言：
: Let a be a constant vector and r = xi + yj + zk.
:
: Ｖｅｒｉｆｙ ｔｈｅ ｇｉｖｅｎ ｉｄｅｎｔｉｔｙ.
: Question: (a cross del) cross r = -2a
:
:
: 歡迎各位回答~
:
: 感謝大家～～
:
:
→
(a ×▽) ×r
→ →
= - r ×(a ×▽)
→ → → → →
= (- r ．▽ + ▽．-r ) a - (-r ． a)▽
→ → → → →
= - r ．▽a - 3a + ▽( r ． a)
→ → → → →
= 0 - 3a + ▽r ．a + r ．▽a
→ →
= -3a + a + 0
→
= -2a
→ →
(▽a 偏微後為0 、 ▽r 為I 與任何向量內積為該向量本身)
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