課程名稱︰工程數學
課程性質︰必修
課程教師︰徐治平
開課學院：工學院
開課系所︰化工系
考試日期（年月日）︰2012/6/22
考試時限（分鐘）：110
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
→ → → → → → → → → → →
1.Show that if A=a1 i +a2 j +a3 k, B=b1 i +b2 j +b3 k, and C=a1 i +a2 j +a3 k,
│a1 a2 a3│
→ → → │ │
then A‧(B×C)=│b1 b2 b3│ (15%)
│ │
│c1 c2 c3│
2.Find the included angle between two planes: x+2y+3x=3 and x-2y-3z=3 (15%)
3.Find the curvature of a circle of radius a (15%)
4.Find the tangent plane and the normal verctor to the surface x^2+y^2-z^2=0
at (1,0,1) (15%)
→ → → →
5.(a)Show that F=(y^2 cos(x)+z^3)i+(2ysin(x)-4)j+(3xz^2+2)k is a conservative
→
field.(10%). (b)Evaluate the scalar poteneial for F (10%).(c) Evaluate the
work done in moving an object in this field from (0,1,-1) to (π/2,-1,2) (5%)
→ → → →
6.Let F=-i+xyzj-y^2k and C be the curve describe by x=t, y=|t|, z=1, -1≦t≦1.
→ →
Evaluate ∫F‧dr
c
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