1 / 21

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.

waseemah-duaa
Download Presentation

The unit normal is given by which of the following?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related