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The unit normal is given by which of the following?

The unit normal is given by which of the following?. 1 2 3 4. 1. 2. 3. 4. Find a unit normal to the plane 4x + y – 2z = 3. 1 2 3 4. 1. 2. 3. 4. Find a unit vector normal to the sphere (x + 3)² + (y – 1)² + 2z² = 5 at (0, 0, 1). 1 2 3 4. 1. 2. 3. 4.

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The unit normal is given by which of the following?

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  1. The unit normal is given by which of the following? 1 2 3 4 1. 2. 3. 4.

  2. Find a unit normal to the plane 4x + y – 2z = 3 1 2 3 4 1. 2. 3. 4.

  3. Find a unit vector normal to the sphere (x + 3)² + (y – 1)² + 2z² = 5 at (0, 0, 1). 1 2 3 4 1. 2. 3. 4.

  4. Which of the following vector fields are conservative? F=xyi + 2y²zj + 3xyzk F=y²i + 2xyj + 2zk F=2x²zi + xyzj - 2xyk F=2yzi + 2xzj + 2xyk

  5. Which of the following statements are true? only depends on the end points of A and B for all C for a conservative field F All gradient fields are conservative

  6. represents: The area beneath the surface z=F(x,y) but above the curve C. The area beneath the surface z=F(x,y) and below the curve C. The area above the surface z=F(x,y) and above the curve C. The area above the surface z=F(x,y) but below the curve C.

  7. Which of the following statements is true? evaluates to a scalar evaluates to a scalar Both of the above evaluate to scalars Neither of the above evaluate to scalars

  8. Find where C is the curve y=x²+2 starting from x=0, y=0 and ending at x=1, y=1 ½ + y 1 + 2y 3 7

  9. Find where, on C, x and y are given in terms of the parameter t by x=2t and y=t²+1 for t varying from 0 to 1. 7/3 14/3 ½ + y

  10. In general True False Don’t Know

  11. F = xyi + y²jFind from (0,0) to (1,3) where C is the curve y = 3x 10 270 ½y + 9 (9/2)y + 1

  12. F = 3xyzi + x²yj – 2xyz²kC is a curve from A=(0,0,0) to B=(1,1,1) given by x=y=z=t, 0≤t≤1. Find . 3/10 3/5 i/4 + j/4– k/5 3i/4 + j/4 – 2k/5

  13. Evaluate where C represents the contour y=x²+1 from (0,1) to (1,2) 1 2 3 4 1. 2. 3. 4.

  14. Find where F = 2x²i + xy²j + xzkand C is the curve y = x², z = x³ from (0,0,0) to (1,1,1) 1 2 3 4 1. 2. 3. 4.

  15. Evaluate where A represents the surface of the unit cube 0≤x≤1, 0≤y≤1, 0≤z≤1 and r = xi + 2yj + 3zk 15 6 3 0

  16. When an electric current flows at a constant rate through a conductor, then the current continuity equation states that . True False Don’t Know

  17. Evaluate where F = 2xyi + xy²zj + z²kand S is the surface of the unit cube 0≤x≤1, 0≤y≤1, 0≤z≤1 1 2 3 4 1. 2. 3. 4.

  18. F = y²i + 3xyjEvaluate where V is the volume under the plane z=x+y+1 and above z=0 for -1≤x≤2, -1≤y≤2 1 2 3 4 1. 2. 4. 3.

  19. Which of the following is Stokes’ Theorem? 1 2 3 4 1. 2. 3. 4.

  20. Which of the following can be obtained from Gauss’ Law? 1 2 3 4 1. 2. 3. 4.

  21. Evaluate 0 8 -2 None of the above around the rectangle 0≤x≤4, 0≤y≤2 using Green’s Theorem

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