The unit normal is given by which of the following?

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

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

Which of the following vector fields are conservative? 1.F=xyi + 2y²zj + 3xyzk 2.F=y²i + 2xyj + 2zk 3.F=2x²zi + xyzj - 2xyk 4.F=2yzi + 2xzj + 2xyk

Which of the following statements are true? 1. only depends on the end points of A and B 2. for all C 3. for a conservative field F 4.All gradient fields are conservative

represents: 1.The area beneath the surface z=F(x,y) but above the curve C. 2.The area beneath the surface z=F(x,y) and below the curve C. 3.The area above the surface z=F(x,y) and above the curve C. 4.The area above the surface z=F(x,y) but below the curve C.

Which of the following statements is true? 1. evaluates to a scalar 2. evaluates to a scalar 3.Both of the above evaluate to scalars 4.Neither of the above evaluate to scalars

Find where C is the curve y=x²+2 starting from x=0, y=0 and ending at x=1, y=1 1.½ + y y

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 /3 2.14/3 3.½ + y

In general 1.True 2.False 3.Don’t Know

F = xyi + y²j Find from (0,0) to (1,3) where C is the curve y = 3x ½y (9/2)y + 1

F = 3xyzi + x²yj – 2xyz²k C is a curve from A=(0,0,0) to B=(1,1,1) given by x=y=z=t, 0≤t≤1. Find. 1.3/10 2.3/5 3.i/4 + j/4– k/5 4.3i/4 + j/4 – 2k/5

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

Find where F = 2x²i + xy²j + xzk and C is the curve y = x², z = x³ from (0,0,0) to (1,1,1)

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

When an electric current flows at a constant rate through a conductor, then the current continuity equation states that. 1.True 2.False 3.Don’t Know

Evaluate where F = 2xyi + xy²zj + z²k and S is the surface of the unit cube 0≤x≤1, 0≤y≤1, 0≤z≤

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

Which of the following is Stokes’ Theorem?

Which of the following can be obtained from Gauss’ Law?

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