16.9: Mazoezi ya Mapitio ya Sura ya 16
- Page ID
- 178916
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Kweli au Uongo? Thibitisha jibu lako kwa ushahidi au mfano wa kukabiliana.
1. Shamba la vector\(\vecs F(x,y) = x^2 y\,\mathbf{\hat i} + y^2 x\,\mathbf{\hat j}\) ni kihafidhina.
- Jibu
- Uongo
2. Kwa uwanja wa vector\(\vecs F(x,y) = P(x,y)\,\mathbf{\hat i} + Q(x,y)\,\mathbf{\hat j} \), ikiwa\(P_y(x,y) = Q_z(x,y)\) katika kanda ya wazi\(D\), basi\(\displaystyle \int_{\partial D} P \,dx + Q \, dy = 0.\)
3. Tofauti ya shamba la vector ni shamba la vector.
- Jibu
- Uongo
4. Ikiwa\(curl \, \vecs F = \vecs 0\), basi\(\vecs F\) ni shamba la vector la kihafidhina.
Chora mashamba ya vector yafuatayo.
5. \(\vecs F(x,y) = \dfrac{1}{2}\,\mathbf{\hat i} + 2x\,\mathbf{\hat j} \)
- Jibu
6.